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ELM: CSU Math Study Guide17 chapters | 147 lessons | 7 flashcard sets

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Lesson Transcript

Instructor:
*Jennifer Beddoe*

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.

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:

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.

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.

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.

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.

And, then I average 3.17 and 3.15 to get 3.16.

Going back again to Step Three, I divide my original number 10 by my latest average of 3.16, and when I do that, I get 3.16 again. Because this division gives us the same result, our estimation is finished, and the answer to our problem of 'what is the square root of 10' is 3.16.

Try this second example for yourself:

Estimate the square root of 22 to two decimal places.

Did you get an answer of 4.69? If you did, great! If not, don't despair. Here are the steps we took to get there:

When I solved this problem, my first guess was 4.5 because 22 is between 16, which is 4^2, and 25, which is 5^2.

Next, I divided 22 by 4.5 to get 4.89.

Then, I took the average of 4.5 and 4.89 to get 4.70.

Going back and dividing 22 by 4.70, I got 4.68.

Then, the average of 4.70 and 4.68 is 4.69.

When you divide 22 by 4.69 you get 4.69.

Therefore, the answer to the question, 'what is the square root of 22' is 4.69. Remember, you can always check your answer either on a scientific calculator or by multiplying your answer by itself and see if you end up with the original number.

Not all numbers have **perfect square roots**; some are imperfect, containing fractions or decimals. You can estimate the **imperfect square** root of a number using a guess and check method. It can be used on both small and large numbers. It is fairly quick and can be done using just some simple math.

You'll be able to estimate the imperfect square root of numbers using a step-by-step approach after watching this video lesson.

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ELM: CSU Math Study Guide17 chapters | 147 lessons | 7 flashcard sets

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