Question

is there any genius who can ANS this with explanation *

Answer 1

Given,
a + √b = whole root of 14+6√5

So, a+√b = whole root 14+6√5
= whole root of 9+5+6√5
= whole root of (3)^2 +(√5)^2 + 2*3*√5
= whole root of (3+√5)^2
= √(3+√5)^2
= 3+√5

Therefore,
a + √b = 3+√5

Comparing both sides,
a = 3 and b = 5
Hence,

a + b = 3+5 = 8

Therefore,
(C) 8 is the final answer for your question.

Answer 2

$\sqrt{14 + 6 \sqrt{5} } = a + \sqrt{b}$


=> 14 + 6√5 = (a + √b) ²

=> 14 + 6√5 = a² + b + 2a√b

=> 14 + 2(3√5) = a² + b + 2a√b

Comparing values,

a² + b = 14 [neglect, not of use]
a√b = 3√5

××××××××××××

From a√b = 3√5, we get, a = 3 and √b = √5

So, b = 5

=======================

a + b

=> 3 + 5

=> 8



I hope this will help you


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