Questions: Find the square root. If the square root [ sqrtfrac64169 ] sqrtfrac64169= square (Simplify your answer.)

$Find the square root. If the square root [ sqrtfrac64169 ] sqrtfrac64169= square (Simplify your answer.)$

Transcript text: Find the square root. If the square ro \[ \sqrt{\frac{64}{169}} \] $\sqrt{\frac{64}{169}}=$ $\square$ (Simplify your answer.)

Solution

Solution Steps

To find the square root of a fraction, take the square root of the numerator and the square root of the denominator separately. Simplify the resulting fraction if possible.

Step 1: Calculate the Square Root of the Numerator

The numerator of the fraction is 64. The square root of 64 is calculated as follows: \[ \sqrt{64} = 8 \]

Step 2: Calculate the Square Root of the Denominator

The denominator of the fraction is 169. The square root of 169 is calculated as follows: \[ \sqrt{169} = 13 \]

Step 3: Form the Simplified Fraction

Using the results from Steps 1 and 2, form the fraction: \[ \frac{\sqrt{64}}{\sqrt{169}} = \frac{8}{13} \]

Final Answer

The simplified square root of the fraction $\sqrt{\frac{64}{169}}$ is: \[ \boxed{\frac{8}{13}} \]

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