Calculating with Roots

Calculating with Roots

GCSE(F), GCSE(H),

When calculating with indices, roots may be shown as a fraction.

For example, `4^[1/2]` is the same as √4. A cube root of 4 is shown as `4^frac(1)(3)` .

Examples

1. Calculate `125^frac(1)(3) xx 5^2`. Give your answer without a power.

Answer: 125

`125^frac(1)(3) xx 5^2`

`root(3)125 xx 5^2`

`5 xx 25`

= 125

2. Show that `81^frac(1)(4) xx 9^frac(1)(2) = 9`.

Answer: `81^frac(1)(4) xx 9^frac(1)(2) = 9`

`root(4)81 xx root(2)9 = 9`

`3 xx 3 = 9`

Show all the steps; just showing an answer may lose marks.