Question

If x is a positive real number and x² = 2, then x³ =

Options

• \[\sqrt{2}\]

• 2\[\sqrt{2}\]

• 3\[\sqrt{2}\]

• 4

Answer 1

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`