Chapter 1.3, Problem 3P

Simplify each expression.

$\sqrt{25}$

To determine

To Simplify: The expression $\sqrt{25}$

Answer to Problem 3P

The value of the expression $\sqrt{25}$ is $5$

Explanation of Solution

Given information:

The expression $\sqrt{25}$

Concept and Formula Used:

Rule of exponent and addition and subtraction.

  $a^n=a\times a\times a\times \mathrm{..................}n\text{ times,}\sqrt[n]{a}={\left(a\right)}^{\frac{1}{n}}\&{\left(a^m\right)}^n=a^{mn}$

Calculation:

The given expression is

  $\begin{array}{l}\sqrt{25}\\ \text{Factor 25}\\ \sqrt{25}=\sqrt{5\times 5}\\ \sqrt{25}=\sqrt{5^2}\\ \text{Using }\sqrt[n]{a}={\left(a\right)}^{\frac{1}{n}}\\ \sqrt{25}={\left(5^2\right)}^{\frac{1}{2}}\\ \text{Using }{\left(a^m\right)}^n=a^{mn}\\ \sqrt{25}={\left(5\right)}^{2\times \frac{1}{2}}\\ \sqrt{25}=5^1\\ \sqrt{25}=5\end{array}$

Conclusion:

The value of the expression $\sqrt{25}$ is $5$