Square root of 100 – value and solved examples

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Square root of 100

10 is the square root of 100 because we know that 10 x 10 gives 100. Hence, upon inversing the operation, we get √100 = ±10. The value of √100 is positive or negative but in this article we will consider the positive value only.

How to calculate the square root of 100?

While there are many ways to find the value of a square root, in this article, we will focus on the prime factorisation method to derive the value of √10. Furthermore, we know that 100 is a perfect square number, so we can successfully calculate its square root using the prime factorisation method. 100 is a composite number because it has more than two factors. The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100

Now, we will use prime factorisation to calculate the factors of √100.

Upon factorisation, we get 100 = 2 x 2 x 5 x 5. 

So, √100 = √(2 x 2 x 5 x 5)

The factors include two pairs of the number 2 and two pairs of the number 5; therefore, we can consider each pair as one number to do away with the square root.

√100 = 2 x 5 

√100 = 10

100 is a perfect square and 10 x 10 = 100. So, we can also find the root of 100 by another method, i.e., by inversing the squaring operation. 

√100 = √10²

= 10^2*(1/2)

= 10

So, √100 is 10  

Let us look at the root in correlation with power.

Consider the number’ a’ and a natural number ‘x.’ 

Then, a^x = a * a * a …… (multiplied ‘x’ number of times)

If the value of ‘x’ is 2 and ‘a’ is 4, then 42 = 4 x 4 = 16

This means, ‘4 raised to the power 2’ is 16.

Now, the root is the inverse of power. Therefore, we can also see that 10, when multiplied by itself, gives 100. Hence, if 100 is the square of 10 then 10 is also the square root of 100.

Is √100 a rational or irrational number?

If a number terminates at some point or has a repeating pattern in its decimal part, then it is a rational number. Here, we can see that the value of √100 is 10, i.e., a whole number. Hence, it is a rational number

Facts worth considering

• 100 is itself a rational number because the value of its square root is terminating.
• The value of √100 can be calculated by the prime factorisation method because it is a perfect square. 
• 100 can also have a negative root. 

Illustration

1. Find the radius of circular cardboard if its area is equal to 100π cm2.
Ans: Given, area of circular cardboard = 100π cm²
Let us assume that the radius of the circular cardboard piece = x cm
And the formula for area = πr²
So, 
Πr2 = 100π
r2 = 100
r = √100
r = 10 cm
Therefore, the radius of the circular cardboard is 10 cm.

2. Simplify – √100 + 2√5
Ans: Given, √100 + 2√5
We know that √100 = 10 and √5 = 2.23
We get 
= 10 + 2(2.23)
= 10 + 4.46
= 14.46