How to Find the Square Root by Rounding to the Nearest Tenth

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When solving a square root, you are finding the smallest version of the number that, when multiplied by itself, produces the original number. If the original number is not evenly divided into or has a decimal, the square root also has a decimal. A square root cannot be modified after the original number is established. When you attempt to multiply your modified square root by itself, it yields a different original number.

    Round the original number to the nearest 10th, which is one decimal place to the right of the decimal point. If your original number has more than one number to the right of the decimal point, round the number in the 10th position up or down depending on the value of the number to its right. A value of five or higher rounds the number in the 10th position up and four or lower down. For example, if the original number is 15.37, the number is rounded to the 10th to give you 15.4 because 7 is on the higher end. Do this for as many decimal places as you need.

    Type your original number into a scientific calculator. Make sure the screen is clear of any other numbers or calculations so that the your result appears correct. If you continue on with the example, your display now reads 15.4.

    Hit the square root button on your calculator. It will either have the square root symbol (√) or read "sq rt" for short. The number displayed is the square root of your original number. If you multiplied this answer by itself, you would be back to the original number. For example, the square root of 15.4 is 3.924. You cannot round this number to the nearest 10th after taking the square root. Changing the number will not yield the same original number. To expand on the example, if you rounded the answer to the nearest 10th, 3.9, and squared it, you now have 15.21. There is no way to round the square root to a number that yields 15.4.

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