How to Find the Square of a Number

Co-authored by David Jia and Jessica Gibson

Last Updated: August 16, 2024 References

Need to find the square of a number? Finding a number's square is as simple as multiplying it by itself. To square fractions, find the squares of both the numerator and denominator. Then reduce or simplify the result. Keep reading for helpful tips and examples!

Finding the Square of Any Number

Find the square of any number simply by multiplying the number by itself. The square operation is represented by a superscript 2, meaning a number is raised to the power of 2. For example, when you see $5^{{2}}$ , multiply 5 by itself to get 25, which is 5 squared.

Method 1

Method 1 of 3:

Squaring a Single Digit Number

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1
Learn how to do basic multiplication. When you square a number, you simply multiply the number by itself so it's important to know how to multiply . To make it easier to square commonly used single digits, try to memorize basic times tables . ^{[1]
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- For example, learn how to multiply single digit times tables.
2
Multiply the single digit number by itself. Write down the number you want to square. Remember that when you're squaring a number, you multiply it by the same number, not 2. ^{[2]
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- For example, $5^{{2}}$ is not 5 x 2 = 10. Instead, it's 5 x 5 = 25.
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3
Recognize other terms for squaring a number. If you read word problems asking you to square a number, keep in mind that they may also ask you to raise the number to the 2 power or factor. This is just another way of asking you to square the number. ^{[3]
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- You may also see a problem written as 6^2. This is another way of asking you to square 6.
4
Distinguish between squaring and finding the square root. It's easy to get these terms mixed up, but remember that finding the square root of a number is the opposite of squaring a number. Finding the square root means that you're looking for the number that can be multiplied by itself to get the number in the square. ^{[4]
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- For example, $9^{{2}}$ means 9 x 9 = 81 while √9 = 3 because $3^{{2}}$ is equal to 9.

Method 2

Method 2 of 3:

Squaring Larger Numbers

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Write the problem out. To find the square of a number with more than 1 digit, it will help if you rewrite the problem as a double digit multiplication problem. Start by writing the same number on top of itself. ^{[5]
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- For example, to do $24^{{2}}$ , write 24 x 24.
2
Multiply the number on the bottom ones place by the 1 directly above it. Write a line below the numbers and place the result below the ones space. ^{[6]
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- For example, with 24 x 24, multiply the 4 by 4 to get 16. Write a 6 below the ones space and carry the 1 above the top tens number.
3
Multiply the bottom ones place by the top tens number. Take the same number on the bottom and multiply it by the top tens number. Remember to add the number you carried and write the result below the line. ^{[7]
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- For example, with 24 x 24, multiply 4 by 2 and add the 1 you carried. The result below the line should be 96.
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Put a 0 under the result and multiply the bottom tens number by the top ones. The 0 will act as a placeholder. Write the result of multiplying the bottom tens number by the top ones number next to the 0. ^{[8]
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- For the 24 x 24 example, multiply 2 by 4. You should now see 80 below the 96.
5
Multiply the bottom tens number by the top tens number. If you carried any numbers, remember to add them to your result. Write the result below the line. ^{[9]
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- To finish multiplying 24 by 24, multiply the 2 by 2 to get 4. The result on this line should be 480.
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Add the 2 results to get your answer. If you multiplied a number with 3 or more digits, you'll have more lines to add together. Write the answer from your results to show the square of the number.
- Add 96 + 480 to get the answer for 24 x 24. $24^{{2}}$ = 576.

Method 3

Method 3 of 3:

Squaring Fractions

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Square the numerator . Multiply the top number of the fraction by itself to find its square. Write the result and place the fraction line below it. ^{[10]
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- For example, with ( ⁸ / ₂ ) ² , you'd multiply 8 by 8 to get a numerator of 64.
2
Square the denominator. Multiply the bottom number of the fraction by itself. Write the result of this square below the fraction line. ^{[11]
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- So for ( ⁸ / ₂ ) ² , multiply 2 by 2 to get a denominator of 4.
3
Simplify the result . While you could leave the fraction large or improper, most directions will tell you to simplify or reduce the result. If you have an improper fraction, turn it into a mixed number. ^{[12]
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- For example, ( ⁸ / ₂ ) ² = ( ⁶⁴ / ₄ ) can be simplified to 16 because 4 goes into 64 16 times.

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How do I calculate the square root?

Donagan

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See Calculate a Square Root by Hand .

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√5 is the square of what number?

Donagan

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√5 is the square of plus-or-minus the fourth root of 5.

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What is the square of 25?

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25² = 25)(25) = 625.

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Remember that if you square a negative number, the answer will be positive because the 2 negatives cancel each other out.

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To square a number using a calculator, enter the number x the number. For example, for $4^{{2}}$ , enter 4 x 4 to get 16.

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How to Find the Square of a Number

Finding the Square of Any Number

Steps

Squaring a Single Digit Number

Squaring Larger Numbers

Squaring Fractions

Community Q&A

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Tips

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