Chapter 1.3, Problem 1P

Simplify each expression.

$\sqrt{4}$

To determine

To Simplify: The expression $\sqrt{4}$

Answer to Problem 1P

The value of the expression $\sqrt{4}$ is $2$

Explanation of Solution

Given information:

The expression $\sqrt{4}$

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

  $\begin{array}{l}\sqrt{4}\\ \text{Factor 4}\\ \sqrt{4}=\sqrt{2\times 2}\\ \sqrt{4}=\sqrt{2^2}\\ \text{Using }\sqrt[n]{a}={\left(a\right)}^{\frac{1}{n}}\\ \sqrt{4}={\left(2^2\right)}^{\frac{1}{2}}\\ \text{Using }{\left(a^m\right)}^n=a^{mn}\\ \sqrt{4}={\left(2\right)}^{2\times \frac{1}{2}}\\ \sqrt{4}=2^1\\ \sqrt{4}=2\end{array}$

Conclusion:

The value of the expression $\sqrt{4}$ is $2$