Question

Show that √(75+12√21) = 3√7+2√3, dot square on both sides apply operations only on the left hand side.

Answer 1

Given : √(75+12√21) = 3√7+2√3

To Find : Show that its Equal

Solution:

Let say

√(75+12√21) = 3√7+2√3  = A

LHS = √(75+12√21)  = A

RHS  =  3√7+2√3  = A

Squaring both sides

=> (3√7+2√3 )² = A²

=> (3√7)² + (2√3)² + 2*3√7*2√3 = A²

=> 63 + 12 +  12√21 = A²

=> 75 + 12√21 =A²

Taking square root on both sids

=>  √(75+12√21)  = A

Hence LHS = RHS  = √(75+12√21)  

QED

proved

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