Question

find the square root.
\\(\sqrt{\frac{36}{64}}\\)
\\(\sqrt{\frac{36}{64}} = \square\\) (type an integer or a simplified fraction.)

Explanation:

Step1: Recall square root of fraction rule

The square root of a fraction $\sqrt{\frac{a}{b}}$ is equal to $\frac{\sqrt{a}}{\sqrt{b}}$ (where $a\geq0$ and $b > 0$). So for $\sqrt{\frac{36}{64}}$, we can write it as $\frac{\sqrt{36}}{\sqrt{64}}$.

Step2: Calculate square roots of numerator and denominator

We know that $\sqrt{36}=6$ (because $6\times6 = 36$) and $\sqrt{64}=8$ (because $8\times8 = 64$). So substituting these values into the fraction $\frac{\sqrt{36}}{\sqrt{64}}$, we get $\frac{6}{8}$.

Step3: Simplify the fraction

We can simplify $\frac{6}{8}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So $\frac{6\div2}{8\div2}=\frac{3}{4}$.

Answer:

$\frac{3}{4}$