numerous ptcouncil.netematical operations have actually an inverse, or opposite, operation. Subtraction is the contrary of addition, department is the train station of multiplication, and also so on. Squaring, which we learned about in a previous great (exponents), has actually an inverse too, called "finding the square root." Remember, the square that a number is the number time itself. The perfect squares space the squares the the entirety numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 …

The square source of a number, n, composed is the number that gives n once multiplied through itself. For example, because 10 x 10 = 100

Examples

below are the square roots of all the perfect squares from 1 come 100.

You are watching: What is the opposite of square root Finding square roots of of numbers the aren"t perfect squares without a calculator

1. Estimate - first, get as close together you deserve to by finding 2 perfect square roots her number is between.

2. Division - divide your number by one of those square roots.

3. Average - take it the typical of the an outcome of step 2 and also the root.

4. Usage the result of action 3 come repeat measures 2 and also 3 until you have actually a number that is accurate enough for you.

Example: calculation the square source of 10 () come 2 decimal places.

1. uncover the two perfect square number it lies between.

Solution: 32 = 9 and 42 = 16, so lies between 3 and also 4.

2. division 10 by 3. 10/3 = 3.33 (you can round off her answer)

3. median 3.33 and also 3. (3.33 + 3)/2 = 3.1667

Repeat step 2: 10/3.1667 = 3.1579 Repeat step 3: typical 3.1579 and also 3.1667. (3.1579 + 3.1667)/2 = 3.1623

Try the prize --> Is 3.1623 squared equal to 10? 3.1623 x 3.1623 = 10.0001

If this is accurate enough for you, you have the right to stop! Otherwise, you have the right to repeat procedures 2 and 3.

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Note: There space a number of ways to calculate square roots without a calculator. This is only one of them.

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