The square root of 100 is expressed as √100 in the radical form and as (100)½ or (100)0.5 in the exponent form. The square root of 100 is 10. It is the positive solution of the equation x2 = 100. The number 100 is a perfect square.

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Square Root of 100: 10Square Root of 100 in exponential form: (100)½ or (100)0.5Square Root of 100 in radical form: √100
1.What Is the Square Root of 100?
2.IsSquare Root of 100Rational or Irrational?
3.How to Find the Square Root of 100?
4.Important Notes on Square Root of 100
5.FAQs on Square Root of 100
6.Thinking Out of the Box!

What Is the Square Root of 100?

We know that addition has an inverse operation insubtraction 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 thenumber 100.

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Is the Square Root of 100Rational orIrrational?

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 that100= 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 FactorizationLong division

Square Root of 100By Prime Factorization

Prime factorization is a way of expressing a number as a product of its prime factors. The prime factorization of 100is 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 × 5100= (2× 2 × 5 × 5) = 2 × 5 = 10

Square Root of 100ByLong Division

The value of the square root of 100by 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.

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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 100will 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?