Question

Calculate:

`20^(1/2) xx 5^(1 1/2)`

Answer 1

Given,

`20^(1/2) xx 5^(1 1/2)`

We need to simplify the given terms.

Thus, `20^(1/2) xx 5^(1 1/2)`

= `20^(1/2) xx 5^(3/2)`

= `(4 xx 5)^(1/2) xx 5^(3/2)`

= `4^(1/2) xx 5^(1/2) xx 5^(3/2)`  ...[∴ aⁿ × bⁿ = (ab)ⁿ]

= `(2)^(2 1/2) xx 5^(1/2 + 3/2)`  ...[∴ aⁿ × a^m = a^{n + m}]

= `(2)^(2 xx 1/2) xx 5^2`   ...[∴ (a^m)ⁿ = a^mn]

= 2 × 25

= 50

Hence, the required is 50.