106 is a composite number as the has an ext than 2 factors. The various other two components are 2 and also 53, which can not be simplified any kind of further, making **√**106 one irrational number. In this chapter, we will certainly calculate the square root of 106 through long department method in addition to solved examples. Let us see what the square root of 106 is.

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**Square source of 106**:

**√**106 = 10.295

**Square the 106: 1062**= 11236

1. | What Is the Square root of 106? |

2. | Is Square source of 106 rational or Irrational? |

3. | Important note on Square source of 106 |

4. | How to discover the Square root of 106? |

5. | Thinking the end of the Box! |

6. | FAQs top top Square root of 106 |

## What Is the Square root of 106?

Square root is just an inverse operation of square. The number whose square provides 106, is the square source of 106. The square source of 106 is represented as **√**106.

## Is the Square source of 106 reasonable or Irrational?

Square source of 106 cannot be created in the form of p/q, whereby p and q space integers and q is no equal to 0. The value of **√**106 is 10.295630140987.. Hence, **√**106 is not a rational number.

**Important Notes:**

**√**106 lies in between 10 and 11.106 is no a perfect square, hence,

**√**106 is an irrational number.

## How to find the Square root of 106?

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

### Simplified Radical kind of Square source of 106

106 is a composite number obtained by the product of 2 prime numbers, 2 and 53. Hence, the simplified radical form of **√**106 is **√**106.

We can discover the square root of 106 through the adhering to two methods:

Prime administrate MethodLong department Method### Square root of 106 by element Factorization

106 have the right to be factorized together a product that 2 and also 53, which space prime numbers. Hence, **√**106 = **√**(2 × 53). 2 and also 53 cannot be factorized any further. Thus, the square root of 106 is written as **√**106.

### Square root of 106 by long Division

The worth of square root of 106 by long division method is composed of the complying with steps:

**Step 1**: first we pair the digits of 106 starting with a digit at one"s place. Put a horizontal bar to indicate pairing.

**Step 2**:

**Now we find a number i m sorry on multiplication with itself gives a product of much less than or same to 1. Together we recognize 1 × 1 = 1 = 1.**

**Step 3**:

**Now, we have to lug down 06 and multiply the quotient by 2. This give united state 2. Hence, 2 is the beginning digit the the new divisor.**

**Step 4**: 0 is placed at one"s location of new divisor due to the fact that when 20 is multiply by 0 we acquire 0. The acquired answer now is 20 and we carry down 00.

**Step 5**: The quotient is now 10 and it is multiply by 2. This gives 20, which becomes the beginning digit of the new divisor.

**Step 6**: 2 is placed at one"s ar of brand-new divisor due to the fact that on multiply 202 by 2 we get 404. The prize now acquired is196 and we lug 00 down.

**Step 7**: currently the quotient is 102 when multiply by 2 which gives 204, which will be the beginning digit the the new divisor.

**Step 8**: 9 is put at one"s location of the divisor due to the fact that on multiply 2049 by 9 we gain 18441. The answer derived is 1159 and also we lug 00 down.

**Step 9**: now the quotient is 1029 when multiplied by 2 gives 2058, which will be the beginning digit the the new divisor.

**Step 10**: 5 is put at one"s ar of the divisor due to the fact that on multiply 20585 by 5, we will certainly obtain 102925. The answer acquired is 12975 and also we lug 00 down.

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On repeating the above steps we will attain value the square source of 106 as **√**106 = 10.295630140987..

**Explore square roots using illustrations and also interactive examples**

**Think Tank:**

**√**106?As (-

**√**106)2=106, have the right to we say the -

**√**106 is additionally a square source of 106?