Square Root of 101
Did you know, when we find the square root of a prime number n, the square root of the number "n" is represented as √n and it cannot be simplified any further? Once you understand the basics of square root finding, then you can solve any square rootrelated problem. In this lesson, you will learn about square root of 101 by long division method along with solved examples.
Let us see what the square root of 101 is.
 Square Root of 101:√101 = 10.049
 Square of 101: 101^{2} = 10,201
1.  What Is the Square Root of 101? 
2.  Is Square Root of 101 Rational or Irrational? 
3.  How to Find the Square Root of 101? 
4.  FAQs on Square Root of 101 
What Is the Square Root of 101?
The square root of 101 is the value obtained after performing the operation of square root on 101. The square root of a number is the number that gets multiplied to itself to give the product.
Is the Square Root of 101 Rational or Irrational?
A number that can be expressed as a ratio of two integers, that is, p/q, q is not equal to 0 is called a rational number. Now let us look at the square root of 101.
101 cannot be broken into two such factors which on squaring gives 101. It can be approximately written as a square of 10.049, which is a nonrecurring and nonterminating decimal number. This shows it isn't a perfect square which also proves that the square root of 101 is an irrational number.
Tips and Tricks:
 As 101 is a nonperfect square number, the square root of 101 would be an irrational number. This concludes that square root of any number "n," which is not a perfect square, will always be an irrational number.
How to Find the Square Root of 101?
There are different ways to calculate the square root of 101.
Simplified Radical Form of Square Root of 101
The simplified radical form of square root of 101 is given as √101. As 101 is a prime number hence it cannot simplified any further. Let us now try finding the square root of 101 by the long division method.
Square Root of 101 by Long Division Method
Let us understand the process of finding square root of 101 by long division.
 Step 1: Pair the digits of 101 starting with a digit at one's place. Put a horizontal bar to indicate pairing.
 Step 2: Now we find a number which on multiplication with itself gives a product of less than or equal to 1. As we know 1 × 1 = 1 = 1.
 Step 3: Now, we have to bring down 01 and multiply the quotient by 2. This give us 2. Hence, 2 is the starting digit of the new divisor.
 Step 4: 0 is placed at one's place of new divisor because when 20 is multiplied by 0 we get 0. The obtained answer now is 1 and we bring down 00.
 Step 5: The quotient now becomes 10 and it is multiplied by 2. This gives 20, which then would become the starting digit of the new divisor.
 Step 6: 0 is placed at one's place of new divisor because on multiplying 200 by 0 we get 0. The answer now obtained is 100 and we bring 00 down.
 Step 7: Now the quotient is 100 when multiplied by 2 gives 200, which will be the starting digit of the new divisor.
 Step 8: 4 is placed at one's place of the divisor because on multiplying 2004 by 4 we will get 8016. The answer obtained is 1984 and we bring 00 down.
 Step 9: Now the quotient is 1004 when multiplied by 2 gives 2008, which will be the starting digit of the new divisor.
 Step 10: 9 is placed at one's place of the divisor because on multiplying 20089 by 9, we will get 180801. The answer obtained is 17599.
On continuing further we can estimate the value of square root of 101 to as many places as required.
Explore square roots using illustrations and interactive examples
Important Notes:
 The square root is the inverse operation of squaring.
 Square root of 101 can be expressed as √101 or (101)^{1/2}.
 We can find the square root of 101 or any other number using the radical form and the long division method.
Square Root of 101 Solved Examples

Example 1: Evaluate whether √101 = √100 + √1 or not.
Solution
On simplifying LHS we get, √101 = 10.049.
Similarly on simplifying RHS we get, √100 + √1 = 10 + 1 = 11.
Hence, √101 ≠ √100 + √1. 
Example 2: James wants to buy a new rug for his room. In the store, he finds a square rug that has an area of 101 sq feet. Help James find the length of each side of the rug?
Solution
The area of rug is 101 square feet. And we know that, area of square = (side)^{2}. That means the length of each side of the rug is the square root of its area.The square root of 101 is √101 = 10.05. Hence, the length of each side of the rug is 10.05 feet.
FAQs on Square Root of 101
What is the square root of 101 simplified?
We can simplify it by pulling out the number which is multiplied to itself. But 101 can be only factorized as 101 = 101 × 1. Therefore the square root of 101 simplified is √101.
What is the square root of 101?
The square root of 101 is approximately 10.04987.
Is square root of 101 rational or irrational?
Since 101 is not a perfect square, and therefore it is an irrational number.
How do you find the square root of 101?
We can find the square root of 101 using the long division method.
Is square root of 101 a real number?
Yes, the square root of 101 is a real number.