`sqrt((9261)/(8400))=?`

Answer

To solve the question \( \sqrt{\frac{9261}{8400}} \), we will simplify the expression step by step.

### Step 1: Write the expression
We start with the expression:
\[ \sqrt{\frac{9261}{8400}} \]

### Step 2: Factor the numbers
Next, we need to factor both the numerator and the denominator. We know that:
- \( 9261 = 21^3 \) (since \( 21 \times 21 \times 21 = 9261 \))
- \( 8400 = 100 \times 84 = 100 \times (4 \times 21) = 100 \times 4 \times 21 = 400 \times 21 \)

Thus, we can rewrite the expression as:
\[ \sqrt{\frac{21^3}{400 \times 21}} \]

### Step 3: Simplify the fraction
Now, we can simplify the fraction:
\[ \frac{21^3}{400 \times 21} = \frac{21^2}{400} = \frac{441}{400} \]

### Step 4: Rewrite the square root
Now we can rewrite the square root:
\[ \sqrt{\frac{441}{400}} = \frac{\sqrt{441}}{\sqrt{400}} \]

### Step 5: Calculate the square roots
Next, we calculate the square roots:
- \( \sqrt{441} = 21 \) (since \( 21 \times 21 = 441 \))
- \( \sqrt{400} = 20 \) (since \( 20 \times 20 = 400 \))

Thus, we have:
\[ \frac{\sqrt{441}}{\sqrt{400}} = \frac{21}{20} \]

### Step 6: Final result
The final result is:
\[ \frac{21}{20} = 1.05 \]

Therefore, the answer to \( \sqrt{\frac{9261}{8400}} \) is \( 1.05 \).

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