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Simplify:  51+134+542+16+9\sqrt{51 +\sqrt{134+5\sqrt{42+ \sqrt{16}+\sqrt{9}}}}51+134+542+16​+9​​​​​​
Question

Simplify:  51+134+542+16+9\sqrt{51 +\sqrt{134+5\sqrt{42+ \sqrt{16}+\sqrt{9}}}}​​

A.

197

B.

520

C.

64

D.

8

Correct option is D

Solution: 

=51+134+542+16+9 =51+134+542+4+3 =51+134+35 =51+169  =51+13=64=8=\sqrt{51 +\sqrt{134+5\sqrt{42+ \sqrt{16}+\sqrt{9}}}} \\ \ = \sqrt{51 +\sqrt{134+5\sqrt{42+ 4+ 3}}} \\ \ = \sqrt{51 +\sqrt{134+ 35}} \\ \ = \sqrt{51 +\sqrt{169}} \\ \ \ = \sqrt{51 + 13} \\ = \sqrt{64} \\ =\bf 8​​

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