Solution: The square root of 1849 is 43
Methods
What is the Square Root of 1849?
To start with, let’s review what we define as the square root of a number. A square root of a number is a number that when multiplied by itself gives the original value. So, for instance, the square root of 16 is 4 or √16 = 4, then by definition, we can also say that 4 • 4 is also 16. Now, for the Square Root of 1849, the value is 43. It is noteworthy that the result of a square root can be either a whole number or a decimal.
Is the Square Root of 1849 rational?
Oftentimes when it comes to square roots, it is helpful to know if the value of the square root is rational or irrational. A rational number is when you have a number that can be written as a fraction that divides two integers (as long as the denominator is not 0). Whole numbers can also be rational numbers! So, an irrational number would be a decimal that cannot be written as a fraction and is considered to go on and on with no end (non-terminating). In this case, because the square root of 1849, 43, is a whole number (and not a decimal), we say that 1849 is rational.
How do you find the Square Root of 1849?
There are two main ways to calculate the Square Root of a number: perfect squares and long division. Generally speaking, the first method that uses perfect squares is one of the easier and efficient methods when the number you have is a perfect square. To reiterate, a perfect square occurs when the value of the square root is a whole value. On the other hand, long division is used when the value of the square root is a decimal or not a perfect square.
Our first attempt will be to try to see if we can use perfect squares. So, let's see if we can rewrite 1849 as a product of a number times itself. Well, we know the common perfect square of:
43
×
43
=
1849
43 × 43 = 1849
43 × 43 = 1849
Therefore:
1849
=
4
3
2
=
43
\sqrt{1849} = \sqrt{ 43^{2} } = 43
1849 = 4 3 2 = 43
Thus, helping us arrive at the conclusion that the Square Root of 1849 is 43.
Find The Square Root of Other Numbers
Finding the square root of any number can be done using the same method as shown above. Take a look how to find the square root of these other specific examples, by clicking on the any of the links below:
Square Root of 5
Square Root of 393
Square Root of 2774
Square Root of 4998
Square Root of 4514