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Square Root

What Is the Square Root of 100? What Are the Methods to Find the Square Root of 100?

Written by Prerit Jain

Updated on: 12 Aug 2023

What Is the Square Root of 100? What Are the Methods to Find the Square Root of 100?

What Is the Square Root of 100? What Are the Methods to Find the Square Root of 100?

The square root of 100 is 10. When the number is multiplied by itself it gives the original value. The square root is denoted using the symbol √ in the exponential form it was expressed as (100)0.5 or (100)½ in the radical form it was expressed as √100.

The number 10 when multiplied twice gives 100 and when the number 10 is squared to 102 it gives the original value of 100. The number 100 is a perfect square number because it has a positive whole number. The integer when divided is not equal to zero hence, the number 100 is a rational number.

Methods to find the square root of a number

  • Prime factorization method
  • Long division method
  • Repeated subtraction method

Prime factorization method

Prime factorization is one of the simplest methods used to find the square root of a given number. Take the prime factor of the number as n square the given number we get n2, take a single value, and multiply with the other square. By doing so we will get the square root of the number.

  • Step 1: Find the prime factor of 100
    • 100 = 2 × 2 × 5 × 5
    • √100 = √(2 × 2 × 5 × 5)2
  • Step 2: Find the square of the similar factors by grouping them

√100 = 2 × 5

  • Step 3: By multiplying the common factors we get the square root of the number. Hence, √100 = 10

Long division method

Finding the divisor for the long division method is much simpler than those that are imperfect squares. When 10 is multiplied twice it gives 100 hence, the number 10 is used as a divisor. 

Long division method
Long division method

Hence, √100 = 10

Repeated subtraction method

Using the repeated subtraction method, the square root of the number can be easily solved but consumes time. Hence, the prime factorization and the long division method are widely used to find the square root of the number.

Start subtracting the given number by the first odd number, take the given value, and further subtract the number with the next odd number repeat the step until you reach zero. 

  1. 100-1=99
  2. 99-3 = 96
  3. 96-5= 91
  4. 91-7= 84
  5. 84-9 =75
  6. 75-11= 64
  7. 64-13 = 51
  8. 51-15= 36
  9. 36-17=19
  10. 19-19 = 0

Hence, √100 = 10

Solved examples

Q1: What is the sum of the square of 100 and the square root of 100?
A1: Square of 100 = 10000
The square root of 100 = 10
The sum of the square of 100 and the square root of 100 = 10000+10 = 10010

Q2: Joel wants to find the square root value of 25/100 to help him solve the sum
A2: The √25 = 5.
The √100 = 10
Therefore, the √25/100 = 5/10 = 1/2.

Q3: Solve √100 + 2 √100
A3: The √100 = 10.
Hence 10 + 2 (10).
= 10+20
Hence, √100 + 2 √100=30.

Q4: what is the area of the square whose each side is equal to 10cm?
A4: Area of the square = x2
Here x= 10
Therefore, 102 = 10 × 10 = 100
Hence the area of the square with 10cm = 100 sq. cm

Frequently asked questions

What is the square root of 100?
100 = 2 × 2 × 5 × 5
√100 = √(2 × 2 × 5 × 5)2
The square root of 100 = 10.

Explain why the square root of 100 is a rational number.
When finding the prime factor of 100 we get 102 which is entirely an even power hence all the numbers are positive integers which makes them rational numbers.

What is the value of 100 and the square root of 100?
The square root of 100 is 10
therefore, 100√100 = 100 × 10 = 1000

What is the real value for the square root of 100
When the number 10 is squared twice it gives the actual value.
Hence, the actual value for the 100 = 10

What is the square root of 5?
The number 5 is not a perfect square number, hence the square root of 5 is found using the long division method
Hence, the square root of 5 = 2.23

What is the square root of (-100)?
The square root of minus digits is imaginary numbers or imaginary units which really don’t have a square root.
the square root of the imaginary numbers is written as √100 = 10

Is 100 a perfect square number?
Yes, 100 is a perfect square number. when the number is divided it gives a whole number and not a decimal which makes it fit for a perfect square number.

We hope that we have resolved all your queries related to the square root of 100!

Written by

Prerit Jain

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