Question

radicals
square root of a perfect square monomial
simplify.
\sqrt{16w^{8}}
assume that the variable w represents a positive real number.

Explanation:

Step1: Simplify the numerical part

The square root of 16 is calculated as $\sqrt{16} = 4$ because $4\times4 = 16$.

Step2: Simplify the variable part

For the variable part $w^8$, we use the property of square roots and exponents: $\sqrt{a^n}=a^{\frac{n}{2}}$ (when $a\geq0$). So, $\sqrt{w^8}=w^{\frac{8}{2}} = w^4$.

Step3: Combine the results

Multiply the simplified numerical part and the simplified variable part together: $4\times w^4 = 4w^4$.

Answer:

$4w^4$