Question

Find the square root of $\frac{25}{9}$

Answer 1

Find the square root of $\frac{25}{9}$ using prime factorization method

$\sqrt{\frac{25}{9}}=\frac{\sqrt{25}}{\sqrt{9}}$

We write the prime factors for both the numerator and the denominator

$\Rightarrow$ $\sqrt{\frac{25}{9}}=\frac{\sqrt{5\times 5}}{\sqrt{3\times 3}}$

$\Rightarrow$ $\sqrt{\frac{25}{9}}=\frac{5}{3}$

Hence the square root of $\frac{25}{9}$ is $\frac{5}{3}$