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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:

    1. $\sqrt{81}$
    2. $\sqrt{100}$
    3. $\sqrt{25}$
    4. $\sqrt{400}$
    5. $\sqrt{10000}$
    6. $\sqrt{36}$
    7. $\sqrt{144}$
    8. $\sqrt{169}$
    9. $\sqrt{4}$
    10. $\sqrt{16}$
    11. $\sqrt{64}$
    12. $\sqrt{1936}$

    Answer Key:

Skill:

Common Core Grade Level/Subject

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