Square Roots

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In this lesson, we will look at how to find the square roots of perfect squares and the square roots of non-perfect squares.

Square Roots Of Perfect Squares

The opposite of squaring a number is finding the square root.

We know that 4 squared = 4² = 16. The square root of 16 is the number that can be multiplied by itself to get 16, which is 4.

The symbol used for square root is . (The symbol is also called the radical sign)
= 4 (The square root of 16 is 4).

Notice that –4 is also a square root of 16.
Check: (–4) × (–4) = 16, i.e. (–4)² = 16.

We see that the number 16 has two square roots: a positive square root and a negative square root.

For any positive value x,

We can get the square root of perfect squares in the following way:

Example :

Similarly, for any positive value x,

Example :

Also, take note that

Example:

Example:

Work out the following:

Solution:

The following video shows how to find the square root of perfect squares.

• Show Step-by-step Solutions

Square Roots Of Non-Perfect Squares

Square root of numbers that are not perfect squares would be an irrational number. (Irrational numbers are numbers that cannot be written as fractions. and in decimal form, these numbers go on forever and the same pattern of digits is not repeated.)

For example, = 1.4142…

Usually, we would need to use a calculator to get the square root of a non-perfect square.

However, if you are curious as to how to calculate the square root without a calculator, have a look at the following video.

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