Question

1. Write the following numbers in the form of rational indices,
(A) (1) Square root of seventh power of 64
(2) Cube of fourth root of 57.
(B) (1) 6th root of cube of 102.
(2) Ninth power of fifth root of 2.​

Answer 1

Answer:

1.√−64=8i is the principal square root. −√−64=−8i is the other square root. Note that 8i is not "positive"

2.Cube root of a number can be found by a very simple method which is the prime factorization method. Cube root is denoted by '∛ ' symbol. Example: ∛8 = ∛(2 × 2 × 2) = 2.

3.

StepCube root of 102 can be represented as 3√102. The value of cube root of one is 102. The nearest previous perfect cube is 64 and the nearest next perfect cube is 125 . Cube root of 102 can be represented as 3√102.-by-4

4.The fifth root of a number is the number that would have to be multiplied by itself 5 times to get the original number. For example, the fifth root of 243 is 3 as 3 x 3 x 3 x 3 x 3 is 243. The fifth root of 1,024 is 4, as 4 x 4 x 4 x 4 x 4 is 1,024.

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