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Math Tutor's Solution: The square root of 289 is 17
Methods
What is the Square Root of 289?
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 289, the value is 17. It is noteworthy that the result of a square root can be either a whole number or a decimal.
Is the Square Root of 289 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 289, 17, is a whole number (and not a decimal), we say that 289 is rational.
How do you find the Square Root of 289?
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 289 as a product of a number times itself. Well, we know the common perfect square of:
Therefore:
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:
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