Chapter 9, Problem 1MCT

To determine

To evaluate the given square root.

Answer to Problem 1MCT

  $7$

Explanation of Solution

Given:

  $\sqrt{49}$

Formula used:

Exponent rule: $a^m{a}^n=a^{m+n}$

Radical rule: $\sqrt{a^2}=a$

Calculation:

  $\begin{array}{c}\sqrt{49}=\sqrt{7\cdot 7}\left(\text{Prime factorization of the radicand 49}\right)\\ =\sqrt{7^2}\left(\text{Use}\text{exponent}\text{rule}:a^m{a}^n=a^{m+n}\right)\\ =7\left(\text{U}\text{se}\text{radical}\text{rule}:\sqrt{a^2}=a\right)\end{array}$

Conclusion:

The value of the expression is $7$.