Question

What is the expression in simplest radical form? 384−−−√

Answer 1

Answer:

$8\sqrt{6}$

Step-by-step explanation:

Remember that

$\sqrt{a}=a^{\frac{1}{2}}$

and

$\sqrt{ab}=(ab)^{\frac{1}{2}}=(a)^{\frac{1}{2}}(b)^{\frac{1}{2}}$

we have the number

$\sqrt{384}$

Decompose the number in prime factors

$384=2^{7}3=2^{6}(2)(3)=2^{6}(6)$

substitute

$\sqrt{2^{6}(6)}=(2)^{\frac{6}{2}}(6)^{\frac{1}{2}}=2^3\sqrt{6}=8\sqrt{6}$

therefore

The expression in simplest radical form is $8\sqrt{6}$