Question

The positive square root of 14 +6√5 is ​

Answer 1

14 + 6√5

= 9+ 5 + 6√5 ( splitting 14 as 9+5)

= 3^2 + √5^2+ 6√5

= 3^2 + 6√5 + √5^2

= 3^2+ 2*3*√5+ √5^2

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

Hence

14+6√5 = ( 3+ √5)^2

Square root of 14 + 6√5 = square root of (3+√5)^2

Square root of 14 + 6√ 5 = 3 + √5

Ans : 3+√5