Chapter 9, Problem 1PCT

Evaluate: $-{25}^{\frac{1}{2}}$

To determine

To simplify: The expression $-{25}^{\frac{1}{2}}$.

Answer to Problem 1PCT

The expression $-{25}^{\frac{1}{2}}$ is simplified as $-5$.

Explanation of Solution

Definition used:

If a is a real number and n is an integer with $n\ge 2$, then $a^{\frac{1}{n}}=\sqrt[n]{a}$, provided that $\sqrt[n]{a}$ exists.

Calculation:

The given expression is $-{25}^{\frac{1}{2}}$.

Use the definition to simplify the given expression as follows.

$\begin{array}{c}-{25}^{\frac{1}{2}}=-\sqrt{25}\left[\because a^{\frac{1}{n}}=\sqrt[n]{a}\right]\\ =-\sqrt{5^2}\left[\because 5^2=25\right]\\ =-5\end{array}$

Therefore, the expression $-{25}^{\frac{1}{2}}$ is simplified as $-5$.