How To Find Square Root Of Any Number

Many mathematical operations have an inverse, or opposite, functioning. Subtraction is the opposite of addition, division is the inverse of multiplication, then on. Squaring, which we learned virtually in a previous lesson (exponents), has an changed too, called "finding the foursquare root." Remember, the foursquare of a number is that number times itself. The perfect squares are the squares of the whole numbers: 1, four, 9, 16, 25, 36, 49, 64, 81, 100 …

The foursquare root of a number, due north, written

is the number that gives due north when multiplied by itself. For example,

because 10 ten ten = 100

Examples

Here are the square roots of all the perfect squares from 1 to 100.

Finding square roots of of numbers that aren't perfect squares without a figurer

1. Estimate - start, get as close every bit you can past finding ii perfect foursquare roots your number is between.

2. Divide - dissever your number by 1 of those square roots.

three. Average - take the average of the result of step 2 and the root.

4. Utilize the upshot of step 3 to echo steps 2 and three until you have a number that is accurate enough for you lot.

Example: Calculate the square root of 10 () to 2 decimal places.

1. Find the two perfect foursquare numbers it lies between.

Solution:
iii² = 9 and 4² = 16, so lies between 3 and 4.

two. Split up 10 by 3. 10/3 = three.33 (you can round off your answer)

three. Average 3.33 and 3. (3.33 + iii)/ii = three.1667

Repeat pace 2: 10/three.1667 = 3.1579
Repeat step 3: Boilerplate three.1579 and iii.1667. (3.1579 + 3.1667)/2 = iii.1623

Try the reply --> Is iii.1623 squared equal to x? 3.1623 x 3.1623 = 10.0001

If this is accurate enough for you, you tin finish! Otherwise, you can repeat steps ii and three.

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

back to summit

Source: http://www.math.com/school/subject1/lessons/S1U1L9DP.html

Posted by: kirbycathe1975.blogspot.com

Share this post