Question

Evaluate:

`(sqrt(3) + sqrt(52))^(1/2) (sqrt(52) - sqrt(3))^(1/2)`

Answer 1

Given,

`(sqrt(3) + sqrt(52))^(1/2) (sqrt(52) - sqrt(3))^(1/2)`

We have to evaluate the given terms.

Thus, `(sqrt(3) + sqrt(52))^(1/2) (sqrt(52) - sqrt(3))^(1/2)`

⇒ `(sqrt(52) + sqrt(3))^(1/2) (sqrt(52) - sqrt(3))^(1/2)`  ...[∴ a + b = b + a]

⇒ `[(sqrt(52) + sqrt(3))(sqrt(52) - sqrt(3))]^(1/2)`  ...[∴ aⁿ × bⁿ = (ab)ⁿ]

⇒ `[(sqrt(52))^2 - (sqrt(3))^2]^(1/2)`  ...[∴ (a + b)(a – b) = a² – b²]

⇒ `[52 - 3]^(1/2)`

⇒ `[49]^(1/2)`

⇒ `[7^2]^(1/2) = (7)^(2 xx 1/2)`

⇒ 7

Hence, `(sqrt(3) + sqrt(52))^(1/2) (sqrt(52) - sqrt(3))^(1/2) = 7`