Evaluate the following : (I)`{(5^2+12^2)^(1/2)}^3` (ii) `{(6^2+8^2)^(1/2)}^3`

Explanation

(i)`{(5^2+12^2)^(1/2)}^3`
`=(5^2+12^2)^(1/2times3)`
`=(5^2+12^2)^(3/2)`
`=(25+144)^(3/2)`
`=169^(3/2)`
`=13^(2times3/2)`
`=13^3`
`=2197`
Hence, `2197` is the answer.

(ii) `{(6^2+8^2)^(1/2)}^3`
`={(6^2+8^2)^(1/2)}^3`
`=(36+64)^(1/2times3)`
`=100(3/2)`
`=10^(2times3/2)`
`=10^3`
`=1000`
Hence, `1000` is the answer.