# Alliance

### Square Root Tools

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###### See List of Perfect Squares
A perfect square is a number made by squaring a whole number
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### Finding Square Roots

BASIC: How do I find the square root of a perfect square? (√9 = ?)
ADVANCED: How do I find the square root of any number? (√10 = ?)

###### Basic:

The square root of a number is A NUMBER TIMES ITSELF.

To find the square root of a number, figure out which number times itself equals to that amount.

Therefore √9 = 3

###### How do I find the square root of any number?

By ESTIMATING the closest perfect square to it, DIVIDING it and AVERAGING it.

###### Step 1:

ESTIMATE the two perfect squares in which the number lies. A list of perfect squares will be very useful. 10 lies between 9 and 16. Choose the smallest number. √9=3 So we know our answer is close to 3

###### Step 2:

Divide 10 by 3. 10/3 =3.33

###### Step 3:

Find the average of 3.33 and 3 = (3.33+3)/2. This would be 3.167 3.167 x 3.167 = 10.02 Not accurate enough for you, huh? Proceed to Step 4 for more accuracy.

###### Step 4:

Repeat, repeat, repeat.
Repeat step 2 with the new result: 10/3.167 = 3.157
Now repeat step 3. Find the average of 3.157 and 3.167 = (3.157+3.167)/2 = 3.162

You can check the answer by multiplying it with itself: 3.162x3.162 = 9.998, which is close enough, so we can take it as an answer. If you want higher precision, you can repeat the steps 2 and 3.