Simplify \(\sqrt{160r^2 + \sqrt{71r^4 + \sqrt{100r^8}}}\)

A.

9r2

B.

12\(\sqrt{3r}\)

C.

13r

D.

\(\sqrt{13r}\)

Correct answer is C

\(\sqrt{160r^2 + \sqrt{71r^4 + \sqrt{100r^8}}}\)

Simplifying from the innermost radical and progressing outwards we have the given expression

\(\sqrt{160r^2 + \sqrt{71r^4 + \sqrt{100r^8}}}\) = \(\sqrt{160r^2 + \sqrt{71r^4 + 10r^4}}\)

= \(\sqrt{160r^2 + \sqrt{81r^4}}\)

\(\sqrt{160r^2 + 9r^2}\) = \(\sqrt{169r^2}\)

= 13r