Question

How do you simplify `sqrt32*sqrt144`?

Answer 1

`48sqrt2.`

Explanation:

We use prime factorisation of `32=2^5` and `144=2^4*3^2.`

Hence the expression, `=sqrt32*sqrt144,`
`=(2^5)^(1/2)*(2^4*3^2)^(1/2)`=`(2^4*2)^(1/2)*(2^4*3^2)^(1/2)`
`={(2^4)^(1/2)2^(1/2)}{(2^4)^(1/2)*(3^2)^(1/2)}`=`2^(4*1/2)*2^(1/2)*2^(4*1/2)*3^(2*1/2)=2^2*2^(1/2)*2^2*3^1=4*sqrt2*4*3=48sqrt2.`