Square Root Of 36 Simplified: Explanation And Solution

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Introduction

As a math teacher, I often encounter students struggling with simplifying square roots. One common problem is finding the square root of a perfect square, such as 36. In this article, I will explain the concept of square roots and provide a step-by-step solution on how to simplify the square root of 36.

Square Roots

A square root is a mathematical operation that determines the number that, when multiplied by itself, equals a given number. For example, the square root of 9 is 3 because 3 x 3 = 9. Square roots are represented by the symbol √.

Perfect Squares

A perfect square is a number that is the product of a whole number multiplied by itself. Examples of perfect squares include 1, 4, 9, 16, 25, 36, and so on.

Simplifying Square Roots

To simplify a square root, we need to find the largest perfect square that is a factor of the given number. We then take the square root of the perfect square and multiply it by any remaining factors.

Solution

The square root of 36 can be simplified as follows: Step 1: Find the largest perfect square that is a factor of 36. In this case, it is 6 x 6. Step 2: Take the square root of 6 x 6, which is 6. Step 3: Since there are no remaining factors, the simplified form of the square root of 36 is just 6.

Verification

We can verify that the simplified form of the square root of 36 is correct by squaring 6. 6 x 6 = 36, which confirms that the square root of 36 is indeed 6.

Conclusion

Simplifying square roots can be a challenging task for students. However, by understanding the concept of perfect squares and following the steps outlined in this article, simplifying square roots, such as the square root of 36, can be a breeze.