 # Square Root of 1

## Value of Root 1:

Square root of a number is the value obtained by raising the number to the power ½ . The number obtained by multiplying a number by itself is called a square number. Square and square roots are inverse Mathematical operations. Squares and square roots are used generally in solving quadratic equations and many other Mathematical calculations. Square root is denoted by a symbol ‘√’. Square root of a number ‘x’ is written as √x or x½. Square root of any number has two values: one positive and one negative. However, the magnitude of both the values remain the same. (image will be updated soon)

 Value of Root 1 = + 1 or - 1

1 is the most important element of Mathematics. One or unity in Mathematics is used to represent a single entity in a number, measurement, or calculation. The number ‘1’ has a few peculiar properties which are very important in Mathematical calculations. They are:

• ‘1’ is the number used to represent a single identity.

• ‘1’ is added to any integer to get the immediate successive integer.

• When ‘1’ is subtracted from any integer, the immediate preceding integer is obtained.

• 1 is the multiplicative identity of any number. i.e. When any number is multiplied by itself, the number itself is obtained as the product.

• The multiplicative inverse of any number is the value obtained when ‘1’ is divided by the number.

• When any number is divided by ‘1’, the answer is the number itself.

• When the number is divided by itself, the answer obtained is one.

• The value of any number raised to the power zero is equal to unity.

### Square Root of +1.

It is very important to know how to find the square root of 1 because it gives a clear understanding of finding the square root of other integers.  A positive value of one can be written as 1 x 1 or 12.

So, square root of 1 can be calculated as:

√1 = √12 = ±1

The formula for finding the roots of a quadratic equation can also be used to find the square root of 1.

Let the square of the number ‘x’ be equal to ‘1’. This can be written as:

x2 = 1

x = √1→ (1)

The above equation is a quadratic equation which can be represented in standard form as:

x2 + 0 x - 1 = 0

The above equation is of the form ax2 + bx + c = 0. So, a = 1, b = 0 and c = -1.

The value of ‘x’ can be found using the formula:

$x = \frac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}} = \frac{{ - 0 \pm \sqrt {{0^2} - 4x \times 1 \times - 1} }}{{2 \times 1}} = \pm \frac{{\sqrt 4 }}{2} = \pm \frac{2}{2} = \pm 1$ → (2)

Comparing equations (1) and (2), we can infer that the value of under root 1 is equal to either positive or negative unity.

 Value of root 1 = ±1

Most commonly, the value of under root 1 is taken as positive unity or + 1.

### Value of Square Root of -1:

Root value of ‘-1’ does not exist in theory. It is an imaginary number represented as ‘i’. Root of -1 is generally used to represent complex numbers which include both the real part and the imaginary part. With the knowledge of the square root of negative unity, the root value of any negative number can be found. Square root of -1 is a positive or negative imaginary unit ‘i’. However, in most cases, the value of the root of -1 is taken as a positive imaginary unit ‘i’.

 Root value of - 1 = ± i

### Square Root of First 30 Integers: (graph will be updated soon)

 Number Square Number Square ±1 1 ±16 256 ±2 4 ±17 289 ±3 9 ±18 324 ±4 16 ±19 361 ±5 25 ±20 400 ±6 36 ±21 441 ±7 49 ±22 484 ±8 64 ±23 529 ±9 81 ±24 576 ±10 100 ±25 625 ±11 121 ±26 676 ±12 144 ±27 729 ±13 169 ±28 784 ±14 196 ±29 841 ±15 225 ±30 900

## Values of Square Root 1 to 10 is Listed in the Table Below:

 Number Square root Number Square root 1 1 6 2.4495 2 1.4142 7 2.6458 3 1.7321 8 2.8284 4 2 9 3 5 2.2361 10 3.1623

These values of square root 1 to 10 are depicted on the number line as a square root spiral. (image will be updated soon)

### Example Problems:

1. Solve for p if p2 + 8 = 3

Solution:

p2 + 8 = 3

p2 = 3 - 8

p2 = - 5

p = √-5 = √-1 . √5

p = √5i

1. Find the value of 7√1 - 5√1 + 2√1 using the value of under root 1.

Solution:

Value of √1 = 1

7√1 - 5√1 + 2√1 = 7 (1) - 5 (1) + 2 (1)

= 7 - 5 + 2 = 4.

### Fun Facts:

• ‘I’ is the first unit of imaginary numbers. It is equivalent to number ‘1’ in real numbers.

• When negative unity is raised to the power of odd numbers the answer is -1 and when negative unity is raised to the power of even numbers, the answer is + 1.

• The value of root 1 to any power is equal to 1.