Question

What is the expression in simplest radical form?



384−−−√

Answer 1

`8√(6)`

Explanation:

Remember that

`√(a)=a^{(1)/(2)}`

and

`√(ab)=(ab)^{(1)/(2)}=(a)^{(1)/(2)}(b)^{(1)/(2)}`

we have the number

`√(384)`

Decompose the number in prime factors

`384=2^(7)3=2^(6)(2)(3)=2^(6)(6)`

substitute

`\sqrt{2^(6)(6)}=(2)^{(6)/(2)}(6)^{(1)/(2)}=2^3√(6)=8√(6)`

therefore

The expression in simplest radical form is
`8√(6)`