Square Root of 361

In this article, we will also look at different methods for calculating the square root of 361 using a computer or calculator. We’ll answer some common questions you might have about what the square root is and explore how to calculate the square root of 361.

We can demonstrate the square root of 361 in mathematical form by using the radical symbol, similar to √361. This is commonly referred to as the square root of 361 in radical form.

What is the square root in this case, which is the quantity we will call q, when multiplied by itself will equal 361?

The square root of 361 is equal to q multiplied by q, which is equal to q squared.

Is 361 a Perfect Square?

In mathematics, we classify 361 as a perfect square if its square root yields a whole number.

In this instance, as we will observe in the computations below, we can perceive that 361 is a flawless square.

What is Square Perfect? In our article, you can take a look at a list of 1000 squares and read about them. You can also find out more about perfect squares by reading about them.

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Is The Square Root of 361 Rational or Irrational?

Is it a common question to ask whether the square root of 361 is a rational number, as numbers written as irrational and fractional cannot be rational numbers?

It is an irrational number. If it is not a whole square then it is a rational number. If 361 is a whole square, then a convenient method to verify this is to ascertain if it is.

It is already established that 361 is a perfect square, hence we can deduce that the square root of 361 (√361) is a rational number.

Can the Square Root of 361 Be Simplified?

Let’s simplify the square root of 361 since it is a perfect square, which means it will always result in a whole number that is equal.

√361 = 19..

How to Calculate The Square Root of 361 with a Calculator

To obtain the desired outcome, one should acquire the √x button by inputting the number 361 and subsequently pressing it; this procedure can be performed on the majority of calculators. If you possess a calculator, the easiest method to compute the square root of 361 is by employing said calculator.

√361 = 19.

How to Calculate the Square Root of 361 with a Computer

You can also calculate the square root of 361 using the SQRT function in Google Sheets, Numbers, or Excel on a computer.

The square root of 361 is equal to 19.

What is the Square Root of 361 Written with an Exponent?

Let’s see how to calculate the square root of a number, which can be converted to a base called the fractional exponent.

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The square root of b is equal to the square root of b raised to the power of 1/2.

The square root of 361 is equal to 361½.

How to Find the Square Root of 361 Using Long Division

Before mathematicians knew how to calculate the square root of a number, they found computers and calculators very useful for testing long division problems. Finally, we can use the long division method to calculate the square root of 361.

Step 1

We want to set one decimal because we attach 00 and move from left to right in pairs of two digits, up to 361.

Step 2

In this manner, place a1.at the bottom and1.on the top. The square root of1.equals 1, and the greatest square number that is less than or equal to 3 is 1, commencing with the initial group.


Step 3

Calculate 3 minus1.and put the difference below. Then move down the next set of numbers.


Step 4

Double the number in green on top:1.× 2 = 2. Then, use 2 and the bottom number to make this problem:

2 times a number is less than or equal to 261.

9 is the largest number that we can find through trial and error, and the question marks are the same for each blank.

Now, input 9 at the top:.


The last two steps actually repeat the previous two steps. Notice that the answer shown at the top in green is the square root of 361, accurate to one decimal digit. It’s that! The last two steps actually repeat the previous two steps. Simply add more sets of 00 and more sets of 00 to answer your question, adding decimal places.

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