Lesson 3: Square Roots of Perfect Squares

A square root $$( \sqrt \; )$$ is an operator that is the opposite of squaring a number. The answer to a square root express is the base that with an exponent of 2 will equal the number under the square root.

For example, $$\sqrt{16} \; = 4$$ since $$4^2 = 16$$.

When the answer is a whole number, then the number under the square root is a perfect square or a square number.

For example, 50 is not a perfect square since $$\sqrt{50} \; = 7.07$$.

Expression Perfect Square?
$$\sqrt{64} = 8$$ 64 is a perfect square
$$\sqrt{77} = 8.77$$ 77 is a perfect square
$$\sqrt{12} = 3.46$$ 12 is a perfect square
$$\sqrt{361} = 19$$ 361 is a perfect square

Choose a number to square root:

Since the a square root is the opposite of squaring:

$$\sqrt{3^2} \; = 3$$

$$(\sqrt{5})^2 \; = 5$$

By looking at the factors of $$100$$ we can find the square root:

 $$1 \cdot 100 = 100$$ $$2 \cdot 50 = 100$$ $$4 \cdot 25 = 100$$ $$5 \cdot 20 = 100$$ $$10 \cdot 10 = 100$$

Since $$100 = 10 \cdot 10 = 10^2$$ then $$\sqrt{100} = 10$$.

At this time, do not take the square root of a negative number. You will learn about this later .