The Bahaí calendar is composed of 19 months, each with 19 days. Hence the number of days in a year in this solar calendar is 19 × 19 = 361. Finding the square root is the inverse operation of squaring the number. In this mini-lesson let us learn to calculate the square root of 361 and to express the square root of 361 in the simplest radical form.

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**Square Root of 361**: **√**361 = 19**Square of 361: **3612 = 130,321

1. | What Is the Square Root of 361? |

2. | Is Square Root of 361 Rational or Irrational? |

3. | How to Find the Square Root of 361? |

4. | Thinking Out of The Box! |

5. | Important Notes on Square Root of 361 |

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FAQs on Square Root of 361 |

## What Is the Square Root of 361?

+ 19 × +19 = **√**361 and – 19 × – 19 =** √**361

**√**361 = ± 19

## Is Square Root of 361 Rational or Irrational?

The square root of 361 is a perfect square number. Thus it is a whole number, which could be expressed as a rational number of the form p/q. The square root of 361 is a **rational number.**

## How to Find the Square Root of 361?

The square root of or any number can be calculated in many ways. To mention a few: Prime factorization method, repeated subtraction method and the long division method.

### Square Root of 361 by Repeated Subtraction Method

Any perfect square number is the sum of consecutive odd numbers. Since 361 is a perfect square, it is the sum of consecutive odd numbers. Thus by repeated subtraction we can verify the square root of 361 is 19.

361 – 1 = 360360 – 3 = 357357 – 5 = 352352 – 7 = 345345 – 9 = 336336 – 11 = 325325 – 13 = 312312 – 15 = 297297- 17 = 280280 – 19 = 261261 – 21 = 240240 – 23 = 217217 – 25 = 202202 – 27 = 175175 – 29 = 146146 – 31 = 115115 – 33 = 8282 – 35 = 3737- 37 = 0

We have done the repeated subtraction 19 times. Thus **√**361 = 19.

### Square Root of 361 by the Long Division Method

Let”s see how to find the square root of 361 by the long division method. Here are the desirable steps to be followed.

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Write 361 as 3 61. Divide 3 by 1 and get the remaider as 2. Bring the pair of 61 down. We have 2 61 to be divided now.Multiply the quotient by 2 and have 2x as the new divisor. Find a number in the place of x such that 2x × x gives 61 or less than that. We find 29 × 9 is 261. We obtain the remainder as 0. Thus,** √**361 = 19.

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

**Think Tank**

Do you know that the sum of first 19 odd numbers (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 +19 + 21 + 23 + 25 + 27 + 29 + 31 + 33 + 35 + 37) = 361? You can find this sum without actual addition. Can you try this out with any other perfect square, as well and check for yourself?

**Important Notes**