Square Root Of 96 Simplified

Square Root of 96 How to Find the Square Root of 96? from www.cuemath.com

Introduction

As a professional teacher, one of the areas that students often struggle with is simplifying square roots. In this article, we will focus on the square root of 96 and how to simplify it. We will provide a step-by-step guide to make it easier for students to understand.

What is a Square Root?

A square root is a number that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3 because 3 multiplied by 3 is 9. The symbol used for square root is √.

What is the Square Root of 96?

The square root of 96 is an irrational number, which means it cannot be expressed as a simple fraction. The exact value of the square root of 96 is √96 = 9.79795897.

How to Simplify the Square Root of 96

To simplify the square root of 96, we need to find the largest perfect square that is a factor of 96. The perfect squares are the numbers that result from multiplying a number by itself. The perfect squares less than 96 are 1, 4, 9, 16, 25, 36, 49, 64, and 81.

Step 1:

We start by dividing 96 by 81, which is the largest perfect square that is a factor of 96. The result is 1 with a remainder of 15.

Step 2:

Next, we divide the remainder (15) by the next largest perfect square, which is 9. The result is 1 with a remainder of 6.

Step 3:

We repeat the process by dividing the remainder (6) by the next largest perfect square, which is 4. The result is 1 with a remainder of 2.

Step 4:

Finally, we divide the remainder (2) by the next largest perfect square, which is 1. The result is 2 with no remainder.

The Simplified Form

Now, we can express the square root of 96 as the product of the square root of the perfect squares we found multiplied by the square root of the remainder, which is 2. Therefore, the simplified form of the square root of 96 is: √96 = √81 x √9 x √4 x √2 √96 = 9 x 3 x 2 x √2 √96 = 54√2

Conclusion

In conclusion, the square root of 96 can be simplified by finding the largest perfect square that is a factor of 96 and breaking down the remainder into perfect squares. By following the steps outlined in this article, students can easily simplify square roots and improve their math skills.