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Question
If x is a positive real number and x2 = 2, then x3 =
Options
\[\sqrt{2}\]
2\[\sqrt{2}\]
3\[\sqrt{2}\]
4
Solution
We have to find `x^3`provided `x^2 = 2`. So,
By raising both sides to the power `1/2`
`x^(2 xx 1/2) = 2^(1/2)`
`x^(2 xx 1/2) = sqrt2`
`x= sqrt2`
By substituting `x= sqrt2` in `x^2` we get
`x^2 = (sqrt2)^3`
= `sqrt2 xx sqrt2 xxsqrt2`
= `2sqrt2`
The value of `x^2`is `2sqrt2`
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