How to Solve a Square Root by Calculation

You can calculate square roots on a calculator or by hand on paper.

A square root of a value is the number that can be multiplied by itself to equal that value. Square roots are written with a symbol that resembles a check mark. Calculating a square root is a common task required in basic middle school, high school and college math classes. You also use square roots in upper-level math courses such as algebra and calculus.

Things You'll Need

• Calculator

Instructions

1. Type a value into your calculator.

2. Press the key that has the square root symbol (√) on it. Your answer will be displayed.

3. Calculate a square root by hand on paper by determining if a whole number can be multiplied by itself to reach the given value. For example, if you have 16, you know that 4 is the square root, because 4 times 4 is 16.

4. Solve a square root that is not a perfect square through the process of estimation. For instance, if you're trying to find the square root of 61, you know that 7 times 7 is 49 and 8 times 8 is 64. Therefore, the answer must be between 7 and 8. Since 61 is closer to 64 than to 49, you could try 7.7 times 7.7. When you multiply this out, you will get 59.29. This means that you need to try a larger number. If you multiply 7.8 by 7.8, you will get 60.84, which is close to 61. Tweak this value by adding a 1 in the hundredths place, then multiply 7.81 by 7.81 to get 60.9961, which can be rounded to 61. This means that 7.81 would be the correct answer.

References

• Math: Square Roots
• Fact Monster: Table of Squares and Square Roots

Resources

• Math: Square Root Calculator