Question

radicals
square root of a perfect square monomial
simplify.
\\(\sqrt{49z^{16}}\\)
assume that the variable \\(z\\) represents a positive real number.

Explanation:

Step1: Apply square root property

The square root of a product is the product of the square roots, so $\sqrt{49z^{16}} = \sqrt{49} \cdot \sqrt{z^{16}}$.

Step2: Simplify each square root

We know that $\sqrt{49} = 7$ (since $7^2 = 49$) and for $\sqrt{z^{16}}$, using the property $\sqrt{x^n}=x^{\frac{n}{2}}$ (for $x\geq0$), we get $z^{\frac{16}{2}} = z^8$.

Step3: Multiply the results

Multiply the two simplified parts: $7 \cdot z^8 = 7z^8$.

Answer:

$7z^8$