113 has only two factors, 1 and the number itself (113). Hence, 113 is a prime number. On taking square root of 113, we can see that **√**113 can not be simplified any further. Thus, **√**113 is an irrational number. In this mini-lesson we will learn to find square root of 113 by long division method along with solved examples. Let us see what the square root of 113 is.

**Square Root of 113**:**√**113 = 10.630**Square of 113: 113**= 12,769^{2}

**Table of Contents**

- What Is the Square Root of 113?
- Is Square Root of 113 Rational or Irrational?
- How to Find the Square Root of 113?
- Important Notes
- FAQs on Square Root of 113
- Thinking Out of the Box!
- Solved Examples on Square Root of 113
- Interactive Questions on Square Root of 113

## What Is the Square Root of 113?

The number whose square gives 113, is the square root of 113. As there are no integers whose square will give the value 113. Hence, **√**113 is given as,

**√**113 = 10.630

On squaring 10.630, we get (10.630)^{2} = 112.9969.. which is close to 113 when it is rounded to its nearest value.

## Is the Square Root of 113 Rational or Irrational?

A rational number either has terminating or non-terminating and has a repeating pattern in its decimal part. We can see that **√**113 = 10.63014581273465...This is non-terminating and the decimal part has no repeating pattern. Hence, **√**113 is an irrational number.

## How to Find the Square Root of 113?

There are different methods to find the square root of any number. Click here to know more about the different methods.

### Simplified Radical Form of Square Root of 113

113 is a prime number hence, it has only two factors 1 and 113. Hence, the simplified radical form of **√**113 is **√**113.

### Square Root of 113 by Long Division Method

The square root of 113 can be found using the long division as follows.

**Step 1**: Pair the digits of 113 starting with a digit at one's place. Put a horizontal bar to indicate pairing.**Step 2**:**Step 3**:**Step 4**: 0 is placed at one's place of new divisor because when 20 is multiplied by 0 we get 0. The obtained answer now is 13 and we bring down 00.**Step 5**: The quotient now becomes 10 and it is multiplied by 2. This gives 20, which then would become the starting digit of the new divisor.**Step 6**: 6 is placed at one's place of new divisor because on multiplying 206 by 6 we get 1236. The answer now obtained is 64 and we bring 00 down.**Step 7**: Now the quotient is 106 when multiplied by 2 gives 212, which will be the starting digit of the new divisor.**Step 8**: 3 is placed at one's place of the divisor because on multiplying 2123 by 3 we will get 6369. The answer obtained is 31 and we bring 00 down.**Step 9**: Now the quotient is 1063 when multiplied by 2 gives 2126, which will be the starting digit of the new divisor.**Step 10**: 0 is placed at one's place of the divisor because on multiplying 21260 by 0, we will get 0. The answer obtained is 31 and we bring 00 down.

So far we have got **√**113 = 10.630. On repeating this process further, we get, **√**113 = 10.63014581273465...

**Explore Square roots using illustrations and interactive examples**

**Important Notes:**

- 113 lies between 100 and 121. So on taking the square root on both the sides, we get
**√**113 lies between**√**100 and**√**121 i.e.,**√**113 lies between 10 and 11. - The square root of 113 is irrational. 113 is not a perfect square which makes it difficult to simplify
**√**113 any further.

## FAQs on Square Root of 113

### Can the square root of 113 be simplified?

As 113 is not a perfect square. Hence, it cannot be simplified further.

### What is the square root of 113 rounded to its nearest tenth?

As, **√**113 = 10.630. On rounding square root of 113 to its nearest tenth we get, 10.6.

### Does 113 have a square root?

Yes, 113 has a square root but it is not a whole number.

### What is the value of square root of 113?

As 113 is not a perfect square, its square root is not a whole number. **√**113 = 10.63014581273465(approx)

### Is the square root of 113 rational or irrational?

The square root of 113 is irrational.

### Is square root of 113 a real number?

Yes, the square root of 113 is a real number.

**Think Tank:**

- What is the value of
**√**(-113) ? - Is the value of
**√**(-113) same as -**√**113?

## Square Root of 113 Solved Examples

**Example 1**: Is it possible to fit a carpet of 8 feet length in a room of area 113 square feet?

**Solution**

Let us assume that the length of the room is x feet. Then the area of the room's floor is x^{2} square feet. By the given information:

x^{2 }= 113

x = **√**113 = 10.6 feet (approx)

The length of the room is 10.6 feet. As the length of carpet is lesser than the length of room, it is possible to fit it in a room of area 113 square feet.

**Example 2**: What is the difference between the radii of circles having areas of circles 113π square inches and 100π square inches?

**Solution**

For finding radius of circle having area 113π we use the formula, area = πr^{2} = 113π

r^{2} = 113

**√**r^{2}= **√**113

By calculating the square root of 113 is 10.6 inches.

For finding radius of circle having area 100π we use the formula, area = πr^{2} = 100π

r^{2} = 100

**√**r^{2}= **√**100

By calculating the square root of 100 is 10 inches.

Hence, the difference between the radii of circles having areas of circles 113π square inches and 100π square inches is (10.6 - 10) inches = 0.4 inches.

## Interactive Questions

**Here are a few activities for you to practice. **

**Select/Type your answer and click the "Check Answer" button to see the result.**