Chapter 5.5, Problem 11OE

To determine

To Find: The monomial whose square is $4a^4$

Answer to Problem 11OE

The monomial whose square is $4a^4$ is $2a^2$

Explanation of Solution

Given information:

The square $4a^4$

Concept and Formula Used:

To find the monomial whose square is given find the square root.

Product of numbers with same sign is positive and with different sign is negative.

  ${\left(a^m\right)}^n=a^{mn},{\left(ab\right)}^n=a^n{b}^n$

Calculation:

The given square is $4a^4$

Taking square root

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

Conclusion:

The monomial whose square is $4a^4$ is $2a^2$