Question

Q2.
a) Is the equality √a^4 = a valid for all values of a? Explain.
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Answer 1

The equality is only true for
`a = 0\ and\ 1`, not for all values

Explanation:

Given

`(\sqrt a)^4 = a`

Required

Determine if it is valid

`(\sqrt a)^4 = a`

Evaluate the exponent

`(a^(1)/(2))^4 = a`

`a^(1*4)/(2) = a`

`a^2 = a`

Rewrite as:

`a^2 - a = 0`

Factorize

`a(a- 1) = 0`

`a =0\ or\ a - 1 = 0`

`a =0\ or\ a = 1`

The equality is only true for
`a = 0\ and\ 1`, not for all values