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:
| \(1 \cdot 100 = 100\) |
| \(2 \cdot 50 = 100\) |
| \(4 \cdot 25 = 100\) |
| \(5 \cdot 20 = 100\) |
| \(\boldsymbol{10 \cdot 10 = 100}\) |
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 ☺.