Square Root of 100
Did you know the word hundred was invented in 1920 by nineyearold Milton Sirotta (19111981), nephew of Edward Kasner, a U.S. mathematician? In this minilesson, we will explore the square root of 100 by understanding square root rules, finding square root by long division method, and how to apply them while solving problems. We will also discover interesting facts about them.
 Square Root of 100: √100 = 10
 Square of 100: 100^{2} = 10000
What Is the Square Root of 100?
We know that addition has an inverse operation in subtraction and multiplication has an inverse operation in the division. Similarly, finding the square root is an inverse operation of squaring. The square root of 100 is the number that gets multiplied to itself to give the number 100.
Look at the image below.
Is the Square Root of 100 Rational or Irrational?
A rational number is a number that can be expressed in the form of p/q, where p and q are integers and q is not equal to 0. We already found that √100 = 10. The number 10 is a rational number. So, the square root of 100 is a rational number.
How to Find the Square Root of 100?
We will discuss two methods of finding the square root of 100
 Prime Factorization
 Long division
Square Root of 100 By Prime Factorization
Prime factorization is a way of expressing a number as a product of its prime factors. The prime factorization of 100 is 100 = 2 × 2 × 5 × 5. To find the square root of 100, we take one number from each pair of the same numbers and we multiply them.
100 = 2 × 2 × 5 × 5
√100 = √(2 × 2 × 5 × 5) = 2 × 5 = 10
Square Root of 100 By Long Division
The value of the square root of 100 by long division method consists of the following steps:
 Step 1: Starting from the right, we will pair up the digits by putting a bar above them.
 Step 2: Find a number which, when multiplied to itself, gives the product less than or equal to 1. So, the number is 1. Putting the divisor as 1, we get the quotient as 1 and the remainder 0.
 Step 3: Double the divisor and enter it with a blank on its right. Guess the largest possible digit to fill the blank which will also become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the product is less than or equal to the dividend. Divide and write the remainder.
Explore Square roots using illustrations and interactive examples
Important Notes:
 The square root is the inverse operation of squaring.
 We can find the square root of 100 using prime factorization, repeated subtraction, and the long division method.
 The square root of a number is both negative and positive for the same numerical value i.e., the square root of 100 will be 10.
Think Tank:
 We know that (10) × (10) =100. So, can we say that 10 is a square root of 100?
 Can you determine a quadratic equation whose roots are 100 and 100?
Square Root of 100 Solved Examples

Example 1: Tim's teacher asked him to find the square root of 1000 using the square root of 100. Can you help him do this?
Solution
The square root of 100 is 10. Using the property of square root, we can write
√1000 = √(100 × 10) = √(100) × √(10) = 10√10.
Hence, the square root of 1000 is 10√10. 
Example 2: A gardener bought 100 plants. He wants to plant them in such a way that the number of plants in each row and column is the same. How many plants will he plant in each row?
Solution
If the gardener plants an equal number of plants in each row and column, then we need to find a number whose square is 100.
We know that, √100 = 10So, if he has 100 plants, he will plant 10 plants in each row.
Hence, the gardener will plant 10 plants in each row.
FAQs On Square Root of 100
What is the square root of 100?
The square root of 100 is 10
What is the square of 100?
The square of 100 is 10000.
How do you find the square root of 100?
We can find the square root of 16 by using the prime factorization, repeated subtraction and long division.
Is the square root of 100 an irrational number?
Yes, the square root of 100 is a rational number.
The square root of 100 is 10, which is a rational number.
What is the square root of 100 in simplified form?
The square root of 100 in simplified form is √100.