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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 = ?)


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.

Your fluency with the times table with help you. Which whole number times itself equals 9?

how to find square root

Therefore √9 = 3


How do I find the square root of any number?

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

Long Answer:

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.