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 minilesson 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: 361^{2} = 130,321
What Is the Square Root of 361?
 The square root of 361 is 361 raised to the power ½. 361^{½ }= (number × number) ^{½} = (19 × 19) ^{½} = (19^{2}) ^{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, 2^{2} = 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
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.
Square Root of 361 Solved Examples

Example 1: Ria bought 361 flower seedlings to plant them into a square bed. How many rows and columns of seedlings would be there on the square bed?
Solution:
Area of the square bed = rows × columns
Area of the square bed = rows × rows
Rows^{2 }= area ^{ }= 361
Taking square root on both the sides we get,
(rows^{2})^{½ }= (361)^{½}
Rows = √361 = 19
Thus, the seedlings are planted in 19 rows and 19 columns. 
Example 2: Mark bakes as many cakes per as the number of days taken in a month. If he bakes 361 cakes in all, how many cakes has he baked and in how many days?
Solution:
Cakes per day × days taken = total cakes
Number of cakes per day = number of days taken = n
n × n = 361
n^{2 }= 361
n = √361 = 19
Thus, Mark has taken 19 days to bake 19 cakes on each day and has made 361 cakes in all.
FAQs On Square Root of 361
What is the square root of 361?
The square root of 361 is ± 19.
What is the negative square root of 361?
The square root of 361 is negative 19.
361 is the square root of which number?
361 is the square root of 130,321.
Is square root of 361 a rational number?
Square root of 361 is a rational number, because the value of √361 is 19. 19 is expressed as p/q = 19/1.
How to find the square root of √361?
If a number is a perfect square, it is easy to evaluate the square root using the inverse operation of the squaring operation.√361 is a perfect square. √361 can be evaluated using the prime factorization long division method or the repeated subtraction method.
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