What is a Square Root?
Contents
A square root of a number is the number that multiplied by itself will equal the initial number. For example, the square root of 4 is 2 because 2 x 2 = 4.
To understand the square root, firstly understand about square. A square of a number is the number multiply by itself. A Square root is opposite of the squared number.
The Square Root Symbol
In mathematics, square roots are represented by the symbol √.
To find the square root of a number we have to find the number, whose multiplication by itself gives the number for which we have to find the square root.
Therefore, the number that multiplied by itself is the square root of the given number.
How to Find the Square Root of X
Solving for the square root of x, also written √x, can be simplified into three main steps.
x can be written as x1 and 1 can be written as ½ + ½
x
= x1
= x½ + ½
We know that two same bases with exponents when multiplied with each other then there powers add. We can separate the bases again.
= (x1/2)( x1/2)
Therefore √x = x1/2
In power form, a square root is represented by power ½.
Positive & Negative Square Root Calculation Example
In the mathematic terms, the square root of a number ‘a’ is a number ‘b’ implies that
b2 = a.
For example:
We know that, (3)2 = 9 and (-3)2 = 9
√9 = √(3 x 3) = 3
√9 = √(-3 x -3) = -3
3 and -3 are two square roots of 9.
√9 = +-3
Every positive number has two square roots one is positive and the other is negative as we had already seen in the example of √9.
Therefore, √a = +√a and -√a
But, Square root of a negative number does not exist.
√-9 is an imaginary number as √-1 = i (an imaginary number) because the square of a negative or a positive number cannot be negative.
Every positive real number has a unique positive square root and that is denoted by the symbol √.
How to Solve Basic Square Root Equations
Here is a table that shows some basic square root calculations along with their equations.
| Square Root of | Equation | Square Root Calculation |
|---|---|---|
| 1 | √1 = √(1 ×1) | 1 |
| 2 | √1 = √(1 ×2) | 1.414 |
| 3 | √3 = √(3 × 1) | 1.732 |
| 4 | √4 = √(2 ×2) | 2 |
| 5 | √5 = √(5 × 1) | 2.236 |
| 6 | √6 = √(2 × 3) | 2.449 |
| 7 | √7 = √(3 + 4) | 2.646 |
| 8 | √8 =√(2 × 2 × 2) | 2.828 |
| 9 | √9 = √(3 ×3) | 3 |
| 10 | x2 = 10 | 3.162 |
| 12 | √12 = √(3 × 2 × 2) | 3.464 |
| 16 | √16 = √(4 ×4) | 4 |
| 20 | √20 = √(2 × 2 × 5) | 4.472 |
| 25 | √25 = √(5 ×5) | 5 |
| 36 | √36 = √(6 ×6) | 6 |
| 49 | √49 = √(7 ×7) | 7 |
| 50 | √50 = √(2×5×5) | 7.071 |
| 64 | √64 = √(8 ×8) | 8 |
| 81 | √81 = √(9 ×9) | 9 |
| 100 | √100 = √(10 ×10) | 10 |
| 169 | √169 = √(13 × 13) | 13 |
| 225 | √225 = √(5 × 5 × 3 × 3) | 15 |