Estimating Square Roots

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  • 0:05 Square Roots
  • 0:26 Perfect Square Roots
  • 0:50 Square Root of an…
  • 1:23 Estimating the Square Root
  • 4:52 Lesson Summary
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Lesson Transcript
Instructor: Jennifer Beddoe

Jennifer has an MS in Chemistry and a BS in Biological Sciences.

Inverse operations are mathematical operations that undo each other. The square root is the inverse of the squared (or multiplying a number by itself) operation. There is an easy method for estimating the square root of a number, which you will learn in this lesson.

Square Roots

In mathematics, the square root operation is the opposite of squaring a number. To square a number, you multiply that number by itself. To find the square root of a number, you need to find the number that when multiplied by itself equals the original number. The symbol for square root looks like this:


Perfect Square Roots

A perfect square root is a number whose square root is an integer. An integer is a number that is not a fraction or a decimal. For example, the square root of 25 is equal to 5 because 5^2 is 25, and the square root of 121 is equal to 11 because 11^2 is 121.

Square Root of an Imperfect Square

A number whose square root is not an integer is an imperfect square. When finding the square root of these numbers, the answer will not be an integer, but will be a fraction or decimal. For example, the square root of 27 is equal to 5.196, and the square root of 215 is equal to 14 2/3.

To determine the square root of an imperfect square, you can use a calculator. However, you can also estimate the square root of a number.

Estimating the Square Root

Here are the steps to estimating the square root of a number to two decimal places:

Step One - Determine which two perfect squares your number falls between. The answer you are looking for will fall between these two numbers.

Step Two - Take a guess about the number just after the decimal place.

Step Three - Divide the number whose square root you are trying to determine by your guess.

Step Four - Find the average between your guess and the answer to the division problem you did in Step Three.

And lastly, Step Five - Repeat Steps Three and Four until the two numbers you are averaging are the same.

Example Problems

Let's do a few examples; that should help everything make sense:

Estimate the square root of 10 to two decimal places.

Step One - The square root of 9 is equal to 3, and the square root of 16 is equal to 4, so our answer to the square root of 10 will be between 3 and 4.

Step Two - 10 is much closer to 9 than it is to 16, so my first guess on the answer will be 3.2.

For Step Three, I divide 10 by the guess of 3.2, which gives a result of 3.13.

For Step Four, I take the average of 3.2 and 3.13, and I get 3.17.

Now, for Step Five, I repeat Step Three with 3.17. 10 divided by 3.17 is equal to 3.15.

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