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Math Tutor's Solution: The square root of 678 is 26.038
Methods
What is the Square Root of 678?
The definition of the square root of a number is the value that, when multiplied by itself, gives the original number. For example, the square root of 25 is equal to 5, because 5 x 5 = 25. Expressed in a radical form: √25 = 5. Therefore, solving for the Square Root of 678, we find that the square root of 678 is 26.038. Always remember: your answer can be either a whole number or a decimal.
Is the Square Root of 678 irrational?
A math tutor would teach that numbers can be categorized into subsets called rational and irrational numbers. An example of irrational numbers are decimals that have no end or are non-terminating. A common confusion is that because a decimal has no end it is a large number that tends to infinity, whereas that isn’t true.
Take a look at the exponential constant e, e has a value of 2.7182818… and is non-terminating but not a huge value because at the end of the day e will never be greater than 3. On the other hand, rational numbers are decimals that can be written as fractions that divide two integers (as long as the denominator is not 0). Thus, for this problem, since the square root of 678, or 26.038, is a non-terminating decimal, so the square root of 678 is irrational.
Methods to find the Square Root of 678
To begin, there are two ways to calculate the Square Root of a number: Prime Factorization and Long Division. Usually, Prime Factorization is used for perfect squares and the long division is used when the value of the square root is a decimal.
Since we know that 678 is decimal, we know that the appropriate method would be long division. This method works very similar to regular long division except in this method, there are some more rules that help us arrive at the answer. Take a look at this example that walks through in detail about what this method is, how to use it, and provides several solved examples. Therefore, the result after using the long division method is 26.038.
Math Tutor Suggests: 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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