Question

What is the simplified version of the square root of 64/9?

Answer 1

$\sqrt{ \frac{64}{9} } = \frac{8}{3}$

Answer 2

You can distribute square roots between numerator and denominator:

$\sqrt{\dfrac{64}{9}} = \dfrac{\sqrt{64}}{\sqrt{9}}$

Now, the square root of a number $y$ is a number $x$ such that $x^2 = y$

So, $\sqrt{64}$ is a number that, when squared, gives 64. This number is 8, since $8^2 = 64$

For the same reason, $\sqrt{9}=3$

So, you have

$\sqrt{\dfrac{64}{9}} = \dfrac{\sqrt{64}}{\sqrt{9}} = \dfrac{8}{3}$