Math Tutor Explains: Square Root of 1521

A math tutor would explain that the square root of a number is simply the inverse of squaring—it’s the value that, when multiplied by itself, equals the original number. In this guide, we’ll break down what a square root is and how to find its value step by step.

Math Tutor's Solution: The square root of 1521 is 39

Methods

What is the Square Root of 1521?

To start with, let’s review what a math tutor would help 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 1521, the value is 39. It is noteworthy that the result of a square root can be either a whole number or a decimal. 

Is the Square Root of 1521 rational?

A math tutor would explain that when working with square roots, it’s helpful to determine whether the value 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 1521, 39, is a whole number (and not a decimal), we say that 1521 is rational. 

How do you find the Square Root of 1521?

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 1521 as a product of a number times itself. Well, we know the common perfect square of:

39×39=152139 × 39 = 1521

Therefore:

1521=392=39\sqrt{1521} = \sqrt{ 39^{2} } = 39

Thus, helping us arrive at the conclusion that the Square Root of 1521 is 39.

Math Tutor Suggest: 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 at how to find the square root of these other specific examples from our math tutors by clicking on any of the links below:

Square Root of 406

Square Root of 2439

Square Root of 1532

Square Root of 1186

Square Root of 946

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