Question

Reduce the radical 176

Answer 1

Answer:  $\boldsymbol{4\sqrt{11}}$

Work Shown:

$\sqrt{176}\\\\\sqrt{4*44}\\\\\sqrt{4}*\sqrt{44}\\\\2*\sqrt{4*11}\\\\2*\sqrt{4}*\sqrt{11}\\\\2*2*\sqrt{11}\\\\\boldsymbol{4\sqrt{11}}$

The idea is to factor the number such that we pull out perfect square factors. We use the rule that $\sqrt{x*y} = \sqrt{x}*\sqrt{y}$ to help break up the root. We also use the idea that $\sqrt{x^2} = x$ when x is nonnegative.