Simplify. $$ \sqrt{25 z^{14}} $$ Assume that the variable $$ z $$ represents a positive real number.

Question

UpStudy AI · Accepted Answer

We start with the expression

$$
\sqrt{25 z^{14}}.
$$

**Step 1:** Split the square root into the product of two square roots:

$$
\sqrt{25 z^{14}} = \sqrt{25} \cdot \sqrt{z^{14}}.
$$

**Step 2:** Simplify each square root.

- The square root of 25 is

$$
\sqrt{25} = 5.
$$

- For the square root of $$ z^{14} $$, since $$ z $$ is a positive real number, we have

$$
\sqrt{z^{14}} = z^{\frac{14}{2}} = z^7.
$$

**Step 3:** Combine the results:

$$
\sqrt{25 z^{14}} = 5 \cdot z^7 = 5z^7.
$$

Thus, the simplified expression is

$$
5z^7.
$$
The simplified expression is $$ 5z^7 $$.

Simplify. \[ \sqrt{25 z^{14}} \] Assume that the variable \( z \) represents a positive real number.