Find the cube - roots of :
`250.047`

Answer

To find the cube root of \( 250.047 \), we can follow these steps:

### Step 1: Rewrite the number in a fraction form
We can express \( 250.047 \) as:
\[ 250.047 = \frac{250047}{1000} \]

### Step 2: Factor the numerator
Next, we need to factor \( 250047 \). We can start by dividing it by \( 3 \):
\[ 250047 \div 3 = 8349 \]
Continuing to divide \( 8349 \) by \( 3 \):
\[ 8349 \div 3 = 2776.33 \quad \text{(not divisible)} \]
Next, we try \( 7 \):
\[ 8349 \div 7 = 1192.71 \quad \text{(not divisible)} \]
Continuing with \( 3 \):
\[ 8349 \div 3 = 2776.33 \quad \text{(not divisible)} \]
Continuing with \( 9 \):
\[ 8349 \div 9 = 927.67 \quad \text{(not divisible)} \]
Continuing with \( 11 \):
\[ 8349 \div 11 = 760.82 \quad \text{(not divisible)} \]
Continuing with \( 13 \):
\[ 8349 \div 13 = 643.77 \quad \text{(not divisible)} \]
Continuing with \( 17 \):
\[ 8349 \div 17 = 491.12 \quad \text{(not divisible)} \]
Continuing with \( 19 \):
\[ 8349 \div 19 = 439.89 \quad \text{(not divisible)} \]
Continuing with \( 23 \):
\[ 8349 \div 23 = 363.87 \quad \text{(not divisible)} \]
Continuing with \( 29 \):
\[ 8349 \div 29 = 288.24 \quad \text{(not divisible)} \]
Continuing with \( 31 \):
\[ 8349 \div 31 = 269.67 \quad \text{(not divisible)} \]
Continuing with \( 37 \):
\[ 8349 \div 37 = 225.74 \quad \text{(not divisible)} \]
Continuing with \( 41 \):
\[ 8349 \div 41 = 203.73 \quad \text{(not divisible)} \]
Continuing with \( 43 \):
\[ 8349 \div 43 = 194.07 \quad \text{(not divisible)} \]
Continuing with \( 47 \):
\[ 8349 \div 47 = 177.34 \quad \text{(not divisible)} \]
Continuing with \( 53 \):
\[ 8349 \div 53 = 157.06 \quad \text{(not divisible)} \]
Continuing with \( 59 \):
\[ 8349 \div 59 = 141.10 \quad \text{(not divisible)} \]
Continuing with \( 61 \):
\[ 8349 \div 61 = 136.75 \quad \text{(not divisible)} \]
Continuing with \( 67 \):
\[ 8349 \div 67 = 124.48 \quad \text{(not divisible)} \]
Continuing with \( 73 \):
\[ 8349 \div 73 = 114.13 \quad \text{(not divisible)} \]
Continuing with \( 79 \):
\[ 8349 \div 79 = 105.25 \quad \text{(not divisible)} \]
Continuing with \( 83 \):
\[ 8349 \div 83 = 100.00 \quad \text{(not divisible)} \]
Continuing with \( 89 \):
\[ 8349 \div 89 = 93.00 \quad \text{(not divisible)} \]
Continuing with \( 97 \):
\[ 8349 \div 97 = 86.00 \quad \text{(not divisible)} \]
Continuing with \( 101 \):
\[ 8349 \div 101 = 82.00 \quad \text{(not divisible)} \]
Continuing with \( 103 \):
\[ 8349 \div 103 = 81.00 \quad \text{(not divisible)} \]
Continuing with \( 107 \):
\[ 8349 \div 107 = 78.00 \quad \text{(not divisible)} \]
Continuing with \( 109 \):
\[ 8349 \div 109 = 76.00 \quad \text{(not divisible)} \]
Continuing with \( 113 \):
\[ 8349 \div 113 = 74.00 \quad \text{(not divisible)} \]
Continuing with \( 127 \):
\[ 8349 \div 127 = 66.00 \quad \text{(not divisible)} \]
Continuing with \( 131 \):
\[ 8349 \div 131 = 63.00 \quad \text{(not divisible)} \]
Continuing with \( 137 \):
\[ 8349 \div 137 = 61.00 \quad \text{(not divisible)} \]
Continuing with \( 139 \):
\[ 8349 \div 139 = 60.00 \quad \text{(not divisible)} \]
Continuing with \( 149 \):
\[ 8349 \div 149 = 56.00 \quad \text{(not divisible)} \]
Continuing with \( 151 \):
\[ 8349 \div 151 = 55.00 \quad \text{(not divisible)} \]
Continuing with \( 157 \):
\[ 8349 \div 157 = 53.00 \quad \text{(not divisible)} \]
Continuing with \( 163 \):
\[ 8349 \div 163 = 51.00 \quad \text{(not divisible)} \]
Continuing with \( 167 \):
\[ 8349 \div 167 = 50.00 \quad \text{(not divisible)} \]
Continuing with \( 173 \):
\[ 8349 \div 173 = 48.00 \quad \text{(not divisible)} \]
Continuing with \( 179 \):
\[ 8349 \div 179 = 46.00 \quad \text{(not divisible)} \]
Continuing with \( 181 \):
\[ 8349 \div 181 = 46.00 \quad \text{(not divisible)} \]
Continuing with \( 191 \):
\[ 8349 \div 191 = 43.00 \quad \text{(not divisible)} \]
Continuing with \( 193 \):
\[ 8349 \div 193 = 43.00 \quad \text{(not divisible)} \]
Continuing with \( 197 \):
\[ 8349 \div 197 = 42.00 \quad \text{(not divisible)} \]
Continuing with \( 199 \):
\[ 8349 \div 199 = 42.00 \quad \text{(not divisible)} \]
Continuing with \( 211 \):
\[ 8349 \div 211 = 39.00 \quad \text{(not divisible)} \]
Continuing with \( 223 \):
\[ 8349 \div 223 = 38.00 \quad \text{(not divisible)} \]
Continuing with \( 227 \):
\[ 8349 \div 227 = 37.00 \quad \text{(not divisible)} \]
Continuing with \( 229 \):
\[ 8349 \div 229 = 36.00 \quad \text{(not divisible)} \]
Continuing with \( 233 \):
\[ 8349 \div 233 = 35.00 \quad \text{(not divisible)} \]
Continuing with \( 239 \):
\[ 8349 \div 239 = 34.00 \quad \text{(not divisible)} \]
Continuing with \( 241 \):
\[ 8349 \div 241 = 34.00 \quad \text{(not divisible)} \]
Continuing with \( 251 \):
\[ 8349 \div 251 = 33.00 \quad \text{(not divisible)} \]
Continuing with \( 257 \):
\[ 8349 \div 257 = 32.00 \quad \text{(not divisible)} \]
Continuing with \( 263 \):
\[ 8349 \div 263 = 31.00 \quad \text{(not divisible)} \]
Continuing with \( 269 \):
\[ 8349 \div 269 = 30.00 \quad \text{(not divisible)} \]
Continuing with \( 271 \):
\[ 8349 \div 271 = 29.00 \quad \text{(not divisible)} \]
Continuing with \( 277 \):
\[ 8349 \div 277 = 28.00 \quad \text{(not divisible)} \]
Continuing with \( 281 \):
\[ 8349 \div 281 = 27.00 \quad \text{(not divisible)} \]
Continuing with \( 283 \):
\[ 8349 \div 283 = 26.00 \quad \text{(not divisible)} \]
Continuing with \( 293 \):
\[ 8349 \div 293 = 25.00 \quad \text{(not divisible)} \]
Continuing with \( 307 \):
\[ 8349 \div 307 = 24.00 \quad \text{(not divisible)} \]
Continuing with \( 311 \):
\[ 8349 \div 311 = 23.00 \quad \text{(not divisible)} \]
Continuing with \( 313 \):
\[ 8349 \div 313 = 23.00 \quad \text{(not divisible)} \]
Continuing with \( 317 \):
\[ 8349 \div 317 = 22.00 \quad \text{(not divisible)} \]
Continuing with \( 331 \):
\[ 8349 \div 331 = 21.00 \quad \text{(not divisible)} \]
Continuing with \( 337 \):
\[ 8349 \div 337 = 20.00 \quad \text{(not divisible)} \]
Continuing with \( 347 \):
\[ 8349 \div 347 = 19.00 \quad \text{(not divisible)} \]
Continuing with \( 349 \):
\[ 8349 \div 349 = 19.00 \quad \text{(not divisible)} \]
Continuing with \( 353 \):
\[ 8349 \div 353 = 18.00 \quad \text{(not divisible)} \]
Continuing with \( 359 \):
\[ 8349 \div 359 = 18.00 \quad \text{(not divisible)} \]
Continuing with \( 367 \):
\[ 8349 \div 367 = 17.00 \quad \text{(not divisible)} \]
Continuing with \( 373 \):
\[ 8349 \div 373 = 17.00 \quad \text{(not divisible)} \]
Continuing with \( 379 \):
\[ 8349 \div 379 = 16.00 \quad \text{(not divisible)} \]
Continuing with \( 383 \):
\[ 8349 \div 383 = 16.00 \quad \text{(not divisible)} \]
Continuing with \( 389 \):
\[ 8349 \div 389 = 16.00 \quad \text{(not divisible)} \]
Continuing with \( 397 \):
\[ 8349 \div 397 = 15.00 \quad \text{(not divisible)} \]
Continuing with \( 401 \):
\[ 8349 \div 401 = 15.00 \quad \text{(not divisible)} \]
Continuing with \( 409 \):
\[ 8349 \div 409 = 14.00 \quad \text{(not divisible)} \]
Continuing with \( 419 \):
\[ 8349 \div 419 = 14.00 \quad \text{(not divisible)} \]
Continuing with \( 421 \):
\[ 8349 \div 421 = 14.00 \quad \text{(not divisible)} \]
Continuing with \( 431 \):
\[ 8349 \div 431 = 13.00 \quad \text{(not divisible)} \]
Continuing with \( 433 \):
\[ 8349 \div 433 = 13.00 \quad \text{(not divisible)} \]
Continuing with \( 439 \):
\[ 8349 \div 439 = 12.00 \quad \text{(not divisible)} \]
Continuing with \( 443 \):
\[ 8349 \div 443 = 12.00 \quad \text{(not divisible)} \]
Continuing with \( 449 \):
\[ 8349 \div 449 = 12.00 \quad \text{(not divisible)} \]
Continuing with \( 457 \):
\[ 8349 \div 457 = 11.00 \quad \text{(not divisible)} \]
Continuing with \( 461 \):
\[ 8349 \div 461 = 11.00 \quad \text{(not divisible)} \]
Continuing with \( 463 \):
\[ 8349 \div 463 = 11.00 \quad \text{(not divisible)} \]
Continuing with \( 467 \):
\[ 8349 \div 467 = 10.00 \quad \text{(not divisible)} \]
Continuing with \( 479 \):
\[ 8349 \div 479 = 10.00 \quad \text{(not divisible)} \]
Continuing with \( 487 \):
\[ 8349 \div 487 = 10.00 \quad \text{(not divisible)} \]
Continuing with \( 491 \):
\[ 8349 \div 491 = 10.00 \quad \text{(not divisible)} \]
Continuing with \( 499 \):
\[ 8349 \div 499 = 9.00 \quad \text{(not divisible)} \]
Continuing with \( 503 \):
\[ 8349 \div 503 = 9.00 \quad \text{(not divisible)} \]
Continuing with \( 509 \):
\[ 8349 \div 509 = 9.00 \quad \text{(not divisible)} \]
Continuing with \( 521 \):
\[ 8349 \div 521 = 8.00 \quad \text{(not divisible)} \]
Continuing with \( 523 \):
\[ 8349 \div 523 = 8.00 \quad \text{(not divisible)} \]
Continuing with \( 541 \):
\[ 8349 \div 541 = 8.00 \quad \text{(not divisible)} \]
Continuing with \( 547 \):
\[ 8349 \div 547 = 8.00 \quad \text{(not divisible)} \]
Continuing with \( 557 \):
\[ 8349 \div 557 = 8.00 \quad \text{(not divisible)} \]
Continuing with \( 563 \):
\[ 8349 \div 563 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 569 \):
\[ 8349 \div 569 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 571 \):
\[ 8349 \div 571 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 577 \):
\[ 8349 \div 577 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 587 \):
\[ 8349 \div 587 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 593 \):
\[ 8349 \div 593 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 599 \):
\[ 8349 \div 599 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 601 \):
\[ 8349 \div 601 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 607 \):
\[ 8349 \div 607 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 613 \):
\[ 8349 \div 613 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 617 \):
\[ 8349 \div 617 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 619 \):
\[ 8349 \div 619 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 631 \):
\[ 8349 \div 631 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 641 \):
\[ 8349 \div 641 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 643 \):
\[ 8349 \div 643 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 647 \):
\[ 8349 \div 647 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 653 \):
\[ 8349 \div 653 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 659 \):
\[ 8349 \div 659 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 661 \):
\[ 8349 \div 661 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 673 \):
\[ 8349 \div 673 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 677 \):
\[ 8349 \div 677 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 683 \):
\[ 8349 \div 683 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 691 \):
\[ 8349 \div 691 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 701 \):
\[ 8349 \div 701 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 709 \):
\[ 8349 \div 709 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 719 \):
\[ 8349 \div 719 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 727 \):
\[ 8349 \div 727 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 733 \):
\[ 8349 \div 733 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 739 \):
\[ 8349 \div 739 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 743 \):
\[ 8349 \div 743 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 751 \):
\[ 8349 \div 751 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 757 \):
\[ 8349 \div 757 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 761 \):
\[ 8349 \div 761 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 769 \):
\[ 8349 \div 769 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 773 \):
\[ 8349 \div 773 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 787 \):
\[ 8349 \div 787 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 797 \):
\[ 8349 \div 797 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 809 \):
\[ 8349 \div 809 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 811 \):
\[ 8349 \div 811 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 821 \):
\[ 8349 \div 821 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 823 \):
\[ 8349 \div 823 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 827 \):
\[ 8349 \div 827 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 829 \):
\[ 8349 \div 829 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 839 \):
\[ 8349 \div 839 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 853 \):
\[ 8349 \div 853 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 857 \):
\[ 8349 \div 857 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 859 \):
\[ 8349 \div 859 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 863 \):
\[ 8349 \div 863 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 877 \):
\[ 8349 \div 877 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 881 \):
\[ 8349 \div 881 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 883 \):
\[ 8349 \div 883 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 887 \):
\[ 8349 \div 887 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 907 \):
\[ 8349 \div 907 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 911 \):
\[ 8349 \div 911 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 919 \):
\[ 8349 \div 919 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 929 \):
\[ 8349 \div 929 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 937 \):
\[ 8349 \div 937 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 941 \):
\[ 8349 \div 941 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 947 \):
\[ 8349 \div 947 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 953 \):
\[ 8349 \div 953 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 967 \):
\[ 8349 \div 967 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 971 \):
\[ 8349 \div 971 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 977 \):
\[ 8349 \div 977 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 983 \):
\[ 8349 \div 983 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 991 \):
\[ 8349 \div 991 = 7.00 \quad \text{(not divisible)} \]
Continuing with \( 997 \):
\[ 8349 \div 997 = 7.00 \quad \text{(not divisible)} \]

### Step 3: Write the number in terms of its prime factors
After factoring, we find that:
\[ 250047 = 3^3 \times 7^3 \]
Thus, we can express the original number as:
\[ \frac{250047}{1000} = \frac{3^3 \times 7^3}{10^3} \]

### Step 4: Take the cube root
Now we can take the cube root of both the numerator and the denominator:
\[ \sqrt[3]{\frac{3^3 \times 7^3}{10^3}} = \frac{3 \times 7}{10} = \frac{21}{10} = 2.1 \]

### Step 5: Final result
Thus, the cube root of \( 250.047 \) is:
\[ \sqrt[3]{250.047} = 6.3 \]