Question

√(23-8√7)+√(11-4√7)
Pls help

Answer 1

√(23-8√7)+√(11-4√7) = 2

Explanation:

Step1:-

Given Surds √(23-8√7)+√(11-4√7)

now we have to simplify √(23-8√7)

`\sqrt{16+7-2×4√(7) }`

`\sqrt{4^(2)+√(7) ^(2)-2(4)√(7)}`

This is form of
`(a-b)^(2) =a^(2) -2 ab+b^(2)`

`\sqrt[2]{(4-√(7))^(2)  }`

`4-√(7)`.......(1)

Step2:-

we have to simplify √(11-4√7)

`\sqrt{7+4-2(2)√(7) }`

`\sqrt{√((7))^(2)+(2)^(2)  -2(2)√(7)  }`

using formula

`(a-b)^(2) =a^(2) -2 ab+b^(2)`

`\sqrt{(√(7))^(2)-(2)^(2)   }`

`√(7)-2`.....(2)

step3:-

adding (1) and (2) equations and cancelled

we get answer is 2