Square Root of 1
The square root of 1 is expressed as √1 in the radical form and as (1)^{½} or (1)^{0.5} in the exponent form. It is the positive solution of the equation x^{2} = 1.
 Square Root of 1: 1
 Square Root of 1 in exponential form: (1)^{½} or (1)^{0.5}
 Square Root of 1 in radical form: √1
1.  What Is the Square Root of 1? 
2.  Is Square Root of 1 Rational or Irrational? 
3.  How to Find the Square Root of 1? 
4.  FAQs on Square Root of 1 
What Is the Square Root of 1?
The square root is an inverse mathematical operation of a square. As you are aware, exceptional cases are always there. In mathematics, there are too many exceptions we deal with. Look at the multiplication shown below when 1 is multiplied by 1 we get a new number as 1, 1 is a square root of 1, or square of 1 is also 1. This is an exceptional case of a square root of 1.
Is Square Root of 1 Rational or Irrational?
Since √1 = 1 which is rational numbers. Hence, the square root of 1 is rational.
How to Find the Square Root of 1?
There are multiple ways to find square roots. Here you will be learning about the long division method. The value of the square root of 1 by the long division method consists of the following steps. The first step is to think about the number whose square is less than or equal to the number 1, treat this number as the divisor as well as the quotient (1 in this case). Perform the division and see the remainder. In the second step, we get the quotient 1 and in the remainder, we get 0. Hence it is a case of a perfect square.
Explore some square roots of other numbers using illustrations and interactive examples.
Think Tank:
 Can you think what will be the square root of 11 and 111?
Important Notes:
 1 is the only number whose square and the square root are equal.
 1 is neither prime nor composite.
Square Root of 1 Solved Examples

Example 1
Find out the perfect square numbers between 1 to 5. Are the numbers rational or irrational?
Solution
The square root of 1 = 1
The square root of 2 = 1.414
The square root of 3 = 1.732
The square root of 4 = 2
The square root of 5 = 2.236
The perfect square numbers between 1 to 5 are 1 and 4.
The square root of 1 and 4 is a rational number. 
Example 2 Jacob is trying different methods to find the square root of a number. Help him find √1 by prime factorization method.
Solution
Prime factorization of 1 = 1 × 1
Now, the square root of 1 would be the product of 1 digit from each pair.
Therefore, √1 = 1 
Example If the surface area of a sphere is 4π in^{2}. Find the radius of the sphere.
Solution:
Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr^{2} = 4π in^{2}
⇒ r = ±√1 in
Since radius can't be negative,
⇒ r = √1
The square root of 1 is 1.
⇒ r = 1 in
FAQs on the Square Root of 1
What is the Value of the Square Root of 1?
The square root of 1 is 1.
If the Square Root of 1 is 1. Find the Value of the Square Root of 0.01.
Let us represent √0.01 in p/q form i.e. √(1/100) = 0.01/10 = 0.1. Hence, the value of √0.01 = 0.1
What is the Square Root of 1?
The square root of 1 is an imaginary number. It is also written as √1 = i
where i = √1 and it is called the imaginary unit.