As a beginner in mathematics, one of the fundamental concepts that you will come across is square roots. A square root is a number that, when multiplied by itself, gives the original number. For example, the square root of 64 is 8, since 8 x 8 = 64. In this guide, we will explore the concept of square roots and provide you with easy-to-follow steps to help you discover the square root of 64.

To begin, let’s take a closer look at what a square root is. As mentioned earlier, a square root is the number that, when multiplied by itself, results in the original number. In mathematical terms, the square root of x is denoted by √x. For instance, the square root of 9 is √9 or 3 since 3 x 3 = 9.

Now, let’s focus on finding the square root of 64. To do this, we can use different methods, including using a calculator, approximation, or simplification by factoring. Let’s explore these methods in detail.

Using a Calculator

One of the simplest methods of finding the square root of 64 is by using a calculator. Most calculators have a square root button, which makes it easy to find square roots. To find the square root of 64 using a calculator, follow these simple steps:

1. Turn on your calculator and make sure it’s in the standard mode.

2. Enter 64 into the calculator.

3. Press the square root (√) button.

4. The calculator should show the answer, which is 8.

That’s it. Using a calculator is the easiest way to get the square root of any number, including 64.

Approximation

Another method of finding the square root of 64 is through approximation. This method involves estimating the value of the square root. Although not as accurate as other methods, approximation can give you an idea of what the square root of 64 could be. Here’s how to use approximation to find the square root of 64:

1. Identify the perfect squares closest to 64. In this case, the two closest perfect squares are 49 and 81.

2. Estimate the halfway point between these perfect squares. In this case, the halfway point is 65/2 or 32.5.

3. Divide 64 by your estimated number (32.5). This gives 1.969.

4. Now, average your estimate with the result obtained in step 3. (32.5+1.969)/2 = 17.234

5. Repeat steps 3-4 until you get a value that is as accurate as possible.

Using the approximation method, we find that the square root of 64 is approximately 8. However, as mentioned earlier, this method is not very accurate and is only useful if you need a quick estimate.

Simplification by Factoring

Another method of finding the square root of 64 is by using simplification through factoring. This involves breaking down the number into smaller factors, which can make it easier to find the square root. Here’s how to use simplification by factoring to find the square root of 64:

1. Start by identifying the prime factors of 64. The prime factors of 64 are 2x2x2x2x2x2 or 2^6.

2. Rewrite the number as a product of its prime factors: √(2x2x2 x 2x2x2).

3. Simplify each prime factor by taking the square root: 2x2x2 = 2³ and 2x2x2 = 2³

4. Multiply the simplified prime factors: 2³ x 2³ = 8 x 8 = 64.

5. The square root of 64 is 8.

Using simplification by factoring, we can see that the square root of 64 is 8.

Conclusion

In conclusion, finding the square root of 64 is a fundamental concept in mathematics that every beginner should master. Whether you use a calculator, approximation, or simplification by factoring, discovering the square root of 64 is easy and straightforward. With practice, you will gain a better understanding of square roots and other mathematical concepts.