Q. 52 - Intermediate Algebra

Question

What is the difference between $9^2$ and $\sqrt{9}$?

Step-by-Step Solution

Answer

Squaring a number means multiplying it by itself one and square rooting a number means finding a number whose square is the given number.

$$\begin{gathered} 9^2=81 \\ \sqrt{9}=3 \end{gathered}$$

Step 1. Explanation for squaring a number.

We have $9^2$.

Squaring a number means multiplying it by itself one.

So,

$$\begin{gathered} 9^2=9\times 9 \\ =81 \end{gathered}$$

Step 2. Explanation for square rooting a number.

We have $\sqrt{9}$.

Square rooting a number means finding a number whose square is the given number.

So,

$$\begin{gathered} \sqrt{9}=\sqrt{3\times 3} \\ =3 \end{gathered}$$