382 LearnersLast updated on May 26th, 2025
Square root of 100
The square root of 100 is a value “y” such that when “y” is multiplied by itself → y × y, the result is 100. The number 100 has a unique non-negative square root, called the principal square root.
What Is the Square Root of 100?
The square root of 100 is ±10, where 10 is the positive solution of the equation x2 = 100. Finding the square root is just the inverse of squaring a number and hence, squaring 10 will result in 100. The square root of 100 is written as √100 in radical form, where the ‘√’ sign is called the “radical” sign. In exponential form, it is written as (100)1/2
Finding the Square Root of 100
We can find the square root of 100 through various methods. They are:
- Prime factorization method
- Long division method
- Repeated subtraction method
Square Root of 100 By Prime Factorization Method
The prime factorization of 100 can be found by dividing the number by prime numbers and continuing to divide the quotients until they can’t be separated anymore. After factoring 100, make pairs out of the factors to get the square root.
So, Prime factorization of 100 = 2 × 5 ×2 × 5
Square root of 100 = √[2 × 2 ×5 × 5] = 2 × 5= 10
Square Root of 100 By Long Division Method
This method is used for obtaining the square root for non-perfect squares, mainly. It usually involves the division of the dividend by the divisor, getting a quotient and a remainder too sometimes.
Follow the steps to calculate the square root of 100:
Step 1: Write the number 100 and draw a bar above the pair of digits from right to left.
Step 2: Now, find the greatest number whose square is less than or equal to 1. Here, it is 1 because 12=1.
Step 3: now divide 1 by 1 (the number we got from Step 2) such that we get 1 as a quotient, and we get a remainder. Double the divisor 1, we get 2, and then the largest possible number A1=0 is chosen such that when 0 is written beside the new divisor 2, a 2-digit number is formed →20, and multiplying 0 with 20 gives 0, which is less than or equal to 0.
Repeat this process until you reach the remainder of 0.
Step 4: The quotient obtained is the square root of 100. In this case, it is 10.
Square Root of 100 By Subtraction Method
We know that the sum of the first n odd numbers is n2. We will use this fact to find square roots through the repeated subtraction method. Furthermore, we just have to subtract consecutive odd numbers from the given number, starting from 1. The square root of the given number will be a count of the number of steps required to obtain 0. Here are the steps:
Step 1: take the number 100 and then subtract the first odd number from it. Here, in this case, it is 100-1=99
Step 2: we have to subtract the next odd number from the obtained number until it comes zero as a result. Now take the obtained number (from step 1), i.e., 99, and again subtract the next odd number after 1, from 3, i.e., 99-3=96. Like this, we have to proceed further.
Step 3: now we have to count the number of subtraction steps it takes to yield 0 finally. Here, in this case, it takes 10 steps.
So, the square root is equal to the count, i.e., the square root of 100 is ±10.
ommon Mistakes and How to Avoid Them in the Square Root of 100
When we find the square root of 100, we often make some key mistakes, especially when we solve problems related to that. So, let’s see some common mistakes and their solutions
Mistake 1
Misunderstanding symbol
Often when √100 is mistaken as 1002, we square the number 100 and we get the result as 10000. So, understanding of symbol should be clear.
Mistake 2
Ignoring the negative root
Remember that both +10 and -10 are valid square roots of 100 where the principal square root is 10, but -10 is also correct.
Mistake 3
Misinterpreting the square root symbol
√100 refers to the positive principal square root. ±√100 will yield both +10 and -10
Mistake 4
Applying square root to non-perfect squares
You have to confirm that 100 is a perfect square before expecting the root will be an integer.
Mistake 5
Forgetting to check for perfect squares
Check if 100 is a perfect square. Since, 100 = 102., it is confirmed that 100 is a perfect square.
Square Root of 100 Examples
Problem 1
A circle has a radius of 10 cm. Verify if its area is a perfect square or not?
Given, the radius of the circle = 100π cm2
Now, area = πr2 (r is the radius of the circle)
So, πr2 = π(10)2 cm2
= 100π cm2
= 100×3.14 cm2
= 314 cm2
Therefore, the area of the circle is 314 cm, which is not a perfect square.
The area of the circle is 314 cm, which is not a perfect square.
Explanation
We know that, area of a circle = πr2 (r is the radius of the circle). Putting the value of the given radius and found the area, which showed up to be not a perfect square
Problem 2
Find the length of a side of a square whose area is 100 cm^2
Given, the area = 100 cm2
We know that, (side of a square)2 = area of square
Or, (side of a square)2 = 100
Or, (side of a square)= √100
Or, the side of a square = ± 10.
But, the length of a square is a positive quantity only, so, the length of the side is 10 cm.
Answer: 10 cm
Explanation
We know that, (side of a square)2 = area of square. Here, we are given with the area of the square, so, we can easily find out its square root because its Square root is the measure of the side of the square
Problem 3
Simplify the expression: √100 ╳ √100, √100+√100
100 ╳ √100
= √(10 ╳ 10) ╳ √(10 ╳ 10)
= 10 ╳ 10
= 100
√100+√100
= √(10 ╳ 10) + √(10 ╳ 10)
= 10 + 10
= 20
Answer: 100, 20
Explanation
In the first expression, we multiplied the value of the square root of 100 with itself.
In the second expression, we added the value of the square root of 100 with itself.
Problem 4
If y=√100, find y^2
firstly, √100= 10
Now, squaring y, we get,
y2=102=100
or, y2=100
Answer : 100
Explanation
squaring “y” which is same as squaring the value of √100 resulted to 100.
Problem 5
Calculate (√100/5 + √100/2)
√100/5 + √100/2
= 10/5 + 10/2
= 2 + 5
= 7
Answer : 7
Explanation
From the given expression, we first found the value of square root of 100 then solved by simple divisions and then simple addition.
FAQs on Square Root of 100
1.Is 100 a rational number?
2.Is 100 a perfect square or a non-perfect square?
3.Is the square root of 100 a rational or irrational number?
4.How to write square root of 100?
5.How is the square root of 100 used in real life?
6.How does the square root of 100 compare to the square root of other numbers?
7.What is the square root of 100 in decimal form?
Important Glossaries for Square Root of 100
Exponential form: An algebraic expression that includes an exponent. It is a way of expressing the numbers raised to some power of their factors. It includes continuous multiplication involving base and exponent. Ex: 2 × 2 × 2 × 2 = 16 Or, 24 = 16, where 2 is the base, 4 is the exponent
Prime Factorization: Expressing the given expression as a product of its factors. Ex: 48=2 × 2 × 2 × 2 × 3
Prime Numbers: Numbers which are greater than 1, having only 2 factors as →1 and Itself. Ex: 1,3,5,7,....
Rational numbers and Irrational numbers: The Number which can be expressed as p/q, where p and q are integers and q not equal to 0 are called Rational numbers. Numbers which cannot be expressed as p/q, where p and q are integers and q not equal to 0 are called Irrational numbers.
Perfect and non-perfect square numbers: Perfect square numbers are those numbers whose square roots do not include decimal places. Ex: 4,9,25 Non-perfect square numbers are those numbers whose square roots comprise decimal places. Ex :3, 8, 24
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Jaskaran Singh Saluja
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Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
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