Question

Find the square root of $\sf 32 + 4\sqrt{5}$

Answer 1

Solution!!

Let's solve it step-by-step.

$\sf \sqrt{32+4\sqrt{5}}$

Factor out the perfect square.

$\sf \sqrt{4(8+\sqrt{5})}$

Write the expression in exponential form with the base of 2².

$\sf \sqrt{2^{2}(8+\sqrt{5})}$

The root of a product is equal to the product of the roots of each factor.

$\sf \sqrt{2^{2}}\sqrt{8+\sqrt{5}}$

Reduce the index of the radical and exponent with 2.

$\sf \underline{\bold{2\sqrt{8+\sqrt{5}}}}$