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​8−215\sqrt{8 - 2\sqrt{15}}8−215​​​ is equal to:
Question

8215\sqrt{8 - 2\sqrt{15}}​ is equal to:

A.

3 - √5

B.

√5- √3

C.

√5+ √3

D.

5 - √3

Correct option is B

Given:

8215\sqrt{8 - 2\sqrt{15}}​​

Formula Used: 

(ab)2=a22ab+b2(a - b)^2 = a^2 - 2ab + b^2 

Solution:

8215=(5+32×5×3)=(53)2=53\sqrt{8 - 2\sqrt{15}}\\ =\sqrt{(5+3-2\times\sqrt5 \times \sqrt3)}\\= \sqrt{(\sqrt{5} - \sqrt{3})^2}\\ = \sqrt{5} - \sqrt{3}​​

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