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 ☺.