Explanation:
Many mathematical operations have an inverse, or opposite, operation. Subtraction is the opposite of addition, division is the inverse of multiplication, and so on. Squaring, which we learned about in a previous lesson (exponents), has an inverse too, called "finding the square root." Remember, the square of a number is that number times itself. The perfect squares are the squares of the whole numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 …
The square root of a number, n, written
√n the number that gives n when multiplied by itself. For example,
√100=10 because 10 x 10 = 100
Examples
Here are the square roots of all the perfect squares from 1 to 100.
√ 1 = 1 since 1 ² = 1
√ 4 = 2 since 2 ² = 4
√ 9= 3 since 3 ² = 9
√ 16= 4 since 4 ² = 16
√ 25= 5 since 5 ² = 25
√ 36= 6 since 6 ² = 36
√ 49= 7 since 7 ² =29
√ 64= 8 since 8 ² = 64
√ 81= 9 since 9 ² = 81
√ 100= 10 since 10 ² = 100
Finding square roots of of numbers that aren't perfect squares without a calculator
1. Estimate - first, get as close as you can by finding two perfect square roots your number is between.
2. Divide - divide your number by one of those square roots.
3. Average - take the average of the result of step 2 and the root.
4. Use the result of step 3 to repeat steps 2 and 3 until you have a number that is accurate enough for you.
Example: Calculate the square root of 10 () to 2 decimal places.
1. Find the two perfect square numbers it lies between.
Solution:
32 = 9 and 42 = 16, so lies between 3 and 4.
2. Divide 10 by 3. 10/3 = 3.33 (you can round off your answer)
3. Average 3.33 and 3. (3.33 + 3)/2 = 3.1667
Repeat step 2: 10/3.1667 = 3.1579
Repeat step 3: Average 3.1579 and 3.1667. (3.1579 + 3.1667)/2 = 3.1623
Try the answer --> Is 3.1623 squared equal to 10? 3.1623 x 3.1623 = 10.0001
If this is accurate enough for you, you can stop! Otherwise, you can repeat steps 2 and 3.