Square Roots

Just as Division is the opposite of Multiplication and Subtraction is the opposite of Addition,
SQUARE ROOTS are the Opposite of Exponents (^2) power

A SQUARE of a number is: N x N = N^2.  A Square Root is the opposite of a Square ^2.
A CUBE of a number is N x N x N = N^3. A Cubed Root is the opposite of ^3

While many calculators have a Square Root or Cube Root Button, you can also use the Exponent (^ Power)  Button: 
4^2 = 16.    16^(1/2) power = 4

2^3 = 2 x 2 x 2 = 8.  8^(1/3) power is 2

(.5 can also be used for the Square Root or 1/2 Power, BUT since 1/3 is a never ending repeating value, (.3333333...) you cannot use that to get an equivalent answer).

A PERFECT SQUARE is when N is an Integer:
1^2 = 1 x 1 = 1
2^2 = 2 x 2 = 4
3^2 = 3 x 3 = 9
4^2 = 4 x 4 = 16
5^2 = 5 x 5 = 25
6^2 = 6 x 6 = 36
7^2 = 7 x 7 = 49
8^2 = 8 x 8 = 64
9^2 = 9 x 9 = 81
10^2 = 10 x 10 = 100
11^2 = 11 x 11 = 121
12^2 = 12 x 12 = 144
13^2 = 13 x 13 = 169
15^2 = 15 x 15 = 255
20^2 = 20 x 20 = 400

The Square Root of any number that is NOT an Integer is a decimal that does not end and does not repeat.

The Operation Symbol is called the RADICAL.

You can approximate a Square Root of a number since is will fall between two perfect Squares.
You can further approximate it as being closer to the lower or higher number (or in the middle).

Two useful approximations are:
2^.5 = 1414
10^.5 = 3.16

Revised: April 24, 2024