The square root of `(6.25)/(6.76)` is

Options

A. `(24)/(25)`
B. `(25)/(26)`
C. `(27)/(24)`
D. `(25)/(27)`

Answer

To find the square root of \(\frac{6.25}{6.76}\), we can follow these steps:

### Step 1: Remove the Decimals
To simplify the calculation, we can remove the decimals by multiplying both the numerator and the denominator by 100.

\[ \frac{6.25}{6.76} = \frac{6.25 \times 100}{6.76 \times 100} = \frac{625}{676} \]

### Step 2: Factor the Numerator and Denominator
Next, we will factor both the numerator (625) and the denominator (676).

**Numerator (625):**
- 625 can be divided by 5:
- \(625 \div 5 = 125\)
- 125 can also be divided by 5:
- \(125 \div 5 = 25\)
- 25 can be divided by 5:
- \(25 \div 5 = 5\)
- Finally, 5 can be divided by 5:
- \(5 \div 5 = 1\)

So, the prime factorization of 625 is:
\[ 625 = 5 \times 5 \times 5 \times 5 = 5^4 \]

**Denominator (676):**
- 676 can be divided by 2:
- \(676 \div 2 = 338\)
- 338 can also be divided by 2:
- \(338 \div 2 = 169\)
- 169 can be divided by 13:
- \(169 \div 13 = 13\)
- Finally, 13 can be divided by 13:
- \(13 \div 13 = 1\)

So, the prime factorization of 676 is:
\[ 676 = 2 \times 2 \times 13 \times 13 = 2^2 \times 13^2 \]

### Step 3: Rewrite the Fraction
Now we can rewrite the fraction using the factorizations we found:

\[ \frac{625}{676} = \frac{5^4}{2^2 \times 13^2} \]

### Step 4: Take the Square Root
Now we will take the square root of the fraction:

\[ \sqrt{\frac{625}{676}} = \frac{\sqrt{625}}{\sqrt{676}} = \frac{5^2}{2 \times 13} = \frac{25}{26} \]

### Final Answer
Thus, the square root of \(\frac{6.25}{6.76}\) is:

\[ \frac{25}{26} \]

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