Question

Evaluate:

`(sqrt(50) + sqrt(42))^(1/3) (sqrt(50) - sqrt(42))^(1/3)`

Answer 1

Given,

`(sqrt(50) + sqrt(42))^(1/3) (sqrt(50) - sqrt(42))^(1/3)`

We have to evaluate the given terms.

Thus, `(sqrt(50) + sqrt(42))^(1/3) (sqrt(50) - sqrt(42))^(1/3)`

⇒ `[(sqrt(50) + sqrt(42)) (sqrt(50) - sqrt(42))]^(1/3)`  ...[∴ aⁿ × bⁿ = abⁿ]

⇒ `[(sqrt(50))^2 - (sqrt(42))^2]^(1/3)`  ...[∴ (a + b)(a – b) = a² – b²]

⇒ `[50 - 42]^(1/3)`

⇒ `[8]^(1/3)`

⇒ `[2^3]^(1/3) = 2^(3 xx 1/3)`

⇒ 2

Hence, `(sqrt(50) + sqrt(42))^(1/3) (sqrt(50) - sqrt(42))^(1/3) = 2`