Square Roots
It's helpful to think of square roots as the opposites of squares.
The square of a number is what you get when you multiply a number by itself. The square of $6 = 6^2 = 36$
The square root of a number is the number that you have to multiply by itself to get another number. So, the square root of $36 = \sqrt{36} = 6$
$6 \times 6 = 36$ so the square root of $36 = 6$.
It's easy to find the square roots of perfect squares (perfect squares are numbers whose square roots are whole numbers).
$$\eqalign{\sqrt{0}&=0\\\sqrt{1}&=1\\\sqrt{4}&=2\\\sqrt{9}&=3\\\sqrt{16}&=4\\\sqrt{25}&=5\\\sqrt{36}&=6\\\sqrt{49}&=7\\\sqrt{64}&=8\\\sqrt{81}&=9\\\sqrt{100}&=10\\\sqrt{121}&=11\\\sqrt{144}&=12}$$
Square roots of numbers that are not perfect squares are always decimals. And, they are impossible for most human minds to calculate (without help from a calculator or computer!).
$$\eqalign{\sqrt{0}&=0\\\sqrt{1}&=1\\\sqrt{2}&=1.41421\\\sqrt{3}&=1.73205\\\sqrt{4}&=2\\\sqrt{5}&=2.23607\\\sqrt{6}&=2.44949\\\sqrt{7}&=2.64575\\\sqrt{8}&=2.82843\\\sqrt{9}&=3\\\sqrt{10}&=3.16228\\\sqrt{11}&=3.31662\\\sqrt{12}&=3.4641}$$
To learn how to estimate square roots, see the Estimating Square Roots lesson.
Practice Problems:
Square Roots
Find the square roots:
- $\sqrt{81}$
- $\sqrt{100}$
- $\sqrt{25}$
- $\sqrt{400}$
- $\sqrt{10000}$
- $\sqrt{36}$
- $\sqrt{144}$
- $\sqrt{169}$
- $\sqrt{4}$
- $\sqrt{16}$
- $\sqrt{64}$
- $\sqrt{1936}$
Answer Key: