Question

√(23-8√7)+√(11-4√7)
Pls help

Answer 1

Answer:

√(23-8√7)+√(11-4√7) = 2

Step-by-step explanation:

Step1:-

Given Surds √(23-8√7)+√(11-4√7)

now we have to simplify √(23-8√7)

$\sqrt{16+7-2×4\sqrt{7} }$

$\sqrt{4^{2}+\sqrt{7} ^{2}-2(4)\sqrt{7}}$

This is form of $(a-b)^{2} =a^{2} -2 ab+b^{2}$

$\sqrt[2]{(4-\sqrt{7})^{2}  }$

$4-\sqrt{7}$.......(1)

Step2:-

we have to simplify √(11-4√7)

$\sqrt{7+4-2(2)\sqrt{7} }$

$\sqrt{\sqrt{(7)}^{2}+(2)^{2}  -2(2)\sqrt{7}  }$

using formula

$(a-b)^{2} =a^{2} -2 ab+b^{2}$

$\sqrt{(\sqrt{7)}^{2}-(2)^{2}   }$

$\sqrt{7}-2$.....(2)

step3:-

adding (1) and (2) equations and cancelled

we get answer is 2