## Square Root of 360?

*The square root of 360 is approximately 18.97 when rounded to two decimal places.*

## Finding Square Roots of Perfect Squares

In mathematics, the square root of a number n is defined as the number that, when multiplied by itself, equals n. For example, the square root of 9 is 3, because 3 squared equals 9 (3 x 3 = 9). When the number under the radical is a perfect square, we can calculate its square root through factoring.

Let’s look at finding the square root of 360, which is a perfect square number.

## Understanding Perfect Squares

A perfect square is a number that can be expressed as the product of two equal factors. Some examples of perfect squares:

4 = 2 x 2 9 = 3 x 3 16 = 4 x 4 25 = 5 x 5

Numbers like 360 that have plenty of factors are often perfect squares.

## Factoring 360

To find the square root of 360, we first prime factorize it:

360 = 2 x 2 x 2 x 3 x 3 x 5

Notice 360 has duplicate prime factors of 2, 3, and 5. This indicates 360 is a perfect square.

## Taking One of Each Pair

For a perfect square, the square root is one factor from each pair:

√360 = 2 x 3 x √5

Simplified square root of 360 equals 6√5.

This quickly gives us the square root of 360 by factoring and simplifying. Understanding perfect squares allows us to use their structure to easily evaluate square roots.

## Checking the Work

We can verify the square root is correct by squaring it to see if we get the original number:

(6√5)2 = 360

Since squaring the simplified root gives us back 360, this confirms that the square root of 360 is 6√5.

In summary, the square root of a perfect square can be determined through factoring and taking one factor from each duplicate pair. This allows simplifying square roots of numbers with plenty of factors quickly by leveraging their unique structure.

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