How To Find The Square Root Of 361? - Cuemath

Square Root of 361

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.

• 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
6.	FAQs on Square Root of 361

What Is the Square Root of 361?

• The square root of 361 is 361 raised to the power ½. 361½ = (number × number) ½ = (19 × 19) ½ = (192) ½ = 19
• + 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 = 360
• 360 - 3 = 357
• 357 - 5 = 352
• 352 - 7 = 345
• 345 - 9 = 336
• 336 - 11 = 325
• 325 - 13 = 312
• 312 - 15 = 297
• 297- 17 = 280
• 280 - 19 = 261
• 261 - 21 = 240
• 240 - 23 = 217
• 217 - 25 = 202
• 202 - 27 = 175
• 175 - 29 = 146
• 146 - 31 = 115
• 115 - 33 = 82
• 82 - 35 = 37
• 37- 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.

• 361 has 3 (odd number of) digits. So we put a bar on the first digit and then another bar on the next pair of digits.
• Now, look at the 3 with bar. Find a number whose square is very close to and less than or equal to 3. 1 is such as number (if we take 2, 22 = 4 and it exceeds 3, so we don't take it). So we write 1 in the place of divisor and quotient.
• Now subtract as we do in normal division process. 3 - 1 = 2.
• Note that we carry forward pair of digits (instead of single digit) while finding the square root. So carry forward 61.
• Next step is to double the existing divisor. The existing divisor was 1, making it double, we get 2. Write it in the place of new divisor.
• Now, place a same digit in each of the blanks of 2 _ × _ such that the product is very close to 261 and less than or equal to 261. We can see that 29 × 9 = 261.
• Now, subtract. 261 - 261 = 0.
• Now, the square root of 361 is the number that is in the place of quotient, which is 19. i.e., √361 = 19.

Explore Square roots using illustrations and interactive examples

• Square root of 169
• Square root of 289
• Square root of 324
• Square root of 81
• Square root of 225

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

• The square root of 361 is 19.
• 361 is a perfect square.
• √361 is a rational number.