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Question
Evaluate:
`(sqrt(50) + sqrt(42))^(1/3) (sqrt(50) - sqrt(42))^(1/3)`
Evaluate
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Solution
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`
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