Question

A=√(6-√11)andB=√(6+√11) then find A+B

Answer 1

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Answer 2

Hello.

We have A=√(6-√11), B=√(6+√11).

To find A+B, we should use perfect square identity.

The example is (A+B)²=A²+B²+2AB.

A²=6-√11

B²=6+√11

AB=√(6-√11)(6+√11), or AB=5

A²+B² is 12, 2AB is 10.

Their sum is 24. Therefore, (A+B)²=24.

We know that A>0, B>0. Therefore, A+B>0.

We can observe that A+B is positive root of 24.

Therefore, A+B=2√6.