# Expert Maths Tutoring in the UK

How to Estimate the Square Root of Non-Square Numbers #22
How to Estimate the Square Root of Non-Square Numbers #22

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Square Root of 100

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.

• Square Root of 100: 10
• Square Root of 100 in exponential form: (100)½ or (100)0.5
• Square Root of 100 in radical form: √100
 1 What Is the Square Root of 100? 2 Is Square Root of 100 Rational 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 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

1. 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.

2. 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 = 10

So, if he has 100 plants, he will plant 10 plants in each row.

Hence, the gardener will plant 10 plants in each row.

3. Example: If the surface area of a sphere is 400π in2. Find the radius of the sphere.

Solution:

Let ‘r’ be the radius of the sphere.

⇒ Area of the sphere = 4πr2 = 400π in2
⇒ r = ±√100 in
⇒ r = √100
The square root of 100 is 10.
⇒ r = 10 in

## FAQs on the Square Root of 100

### What is the Value of the Square Root of 100?

The square root of 100 is 10.

### Why is the Square Root of 100 a Rational Number?

Upon prime factorizing 100 i.e. 22 × 52, we find that all the prime factors are in even power. This implies that the square root of 100 is a positive integer. Therefore, the square root of 100 is rational.

### What is the Value of 10 square root 100?

The square root of 100 is 10. Therefore, 10 √100 = 10 × 10 = 100.

### Is the number 100 a Perfect Square?

The prime factorization of 100 = 22 × 52. Here, all the numbers are in the power of 2. This implies that the square root of 100 is a positive integer. Therefore, 100 is a perfect square.

### What is the Square Root of -100?

The square root of -100 is an imaginary number. It can be written as √-100 = √-1 × √100 = i √100 = 10i
where i = √-1 and it is called the imaginary unit.

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