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How to Square a Number: Second Power and Square Roots

how to square a number: square root formula on a notebook with a pencil nearby

Wondering how to square a number? You’ve come to the right place. Here is your intro to squaring numbers, finding square roots, and determining perfect squares.

How to Square a Number

Squaring is multiplying a number times itself. You use the exponent 2 to demonstrate that the number is being squared:

how to square a number example formula

A negative number times a negative number is a positive number. So, regardless of whether a negative or positive number is being squared, the result will always be positive.

Finding the Square Root

Finding square roots is figuring out what value needs to be multiplied by itself to get the original number. Both negative 2 and positive 2 squared equals 4. So, the square root of 4 can either be +2 or -2:

Here’s how we can demonstrate using this math problem:

how to square a number example

You use the square root symbol to show that the root is being taken. Above, the +/- symbol used before the 2 demonstrates that the square root of a number can be positive or negative.

Note: You cannot take the square root of a negative number.

What Are Perfect Squares?

A perfect square is a whole number you take the square root of and end up with a non-decimal, non-fractional integer. The following values are perfect square numbers:

how to square a number: perfect squares

Though you can technically take the square root of any positive number, if the given number is not a perfect square, you'll end up with an improper fraction, mixed number, or decimal number:

improper fraction

How to Square a Number and Take Square Roots

Squaring a number is simply multiplying the value by itself. When you take the square root of a number, you are figuring out what number had to be squared to get the original value.

The process of squaring and square rooting is helpful in all levels of math that deal with exponents, problem solving, and breaking down equations.

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