Answer: [tex]\boldsymbol{4\sqrt{11}}\\\\[/tex]
Work Shown:
[tex]\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}}\\\\[/tex]
The idea is to factor the number such that we pull out perfect square factors. We use the rule that [tex]\sqrt{x*y} = \sqrt{x}*\sqrt{y}[/tex] to help break up the root. We also use the idea that [tex]\sqrt{x^2} = x[/tex] when x is nonnegative.
