Square Root of 1
Do you know? 1 is the only number whose square and the square root is equal to 1 itself. 1 is the smallest natural number and finding square root of 1 is the easiest one. In this minilesson, you will learn about an exceptional case that is the square root of 1. Check out the interesting examples to know more about the square root of 1and we will also calculate the square root of 1 by the long division method and by prime factorization and find out that whether 1 is a perfect square or not.
 Square Root of 1: √1 = 1
 Square of 1: 1² = 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 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. 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 is 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 are1 and 4.
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
FAQs On Square Root of 1
Is 1 a perfect square?
A perfect square is a number that can be expressed as the product of two equal numbers.
Since 1 × 1 = 1, it is a perfect square number.
What is the square root of 1?
The square root of a 1 is 1.
Can square root 1 be negative?
Square root 1 can be negative number.
Is the square root of 1 rational or irrational?
The square root of 1 is a rational number.
Can you write square root of 1 in simplified radical form?
√1 is the least simplified radical form of square root of 1