Simplifying Square Roots: 2 Easy Ways To Express 147

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Mathematics is often viewed as a complex and daunting subject, but it doesn't have to be. One fundamental concept in mathematics is the square root, which can be intimidating at first, but with the right approach, it can be simplified and made more accessible. In this article, we will explore two easy ways to express 147, a number that is not a perfect square, using square roots.

The concept of square roots is essential in mathematics, particularly in algebra and geometry. It is used to find the length of the side of a square, given its area. For instance, if a square has an area of 16, its side length is the square root of 16, which is 4. However, not all numbers have a perfect square root. In such cases, we need to simplify the square root to make it easier to work with.

Understanding Square Roots

Before we dive into simplifying square roots, it's essential to understand what they are. A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4 because 4 multiplied by 4 equals 16. However, not all numbers have a perfect square root, and in such cases, we need to simplify the square root.

What is Simplifying Square Roots?

Simplifying square roots involves breaking down a complex square root into a simpler form. This is particularly useful when dealing with numbers that are not perfect squares. By simplifying the square root, we can make it easier to work with and perform calculations.

Method 1: Prime Factorization

One way to simplify square roots is by using prime factorization. This involves breaking down a number into its prime factors and then grouping them in pairs. For example, let's simplify the square root of 147 using prime factorization.

First, we need to find the prime factors of 147:

147 = 3 × 7 × 7

Next, we group the prime factors in pairs:

147 = 3 × (7 × 7)

Now, we can simplify the square root:

√147 = √(3 × 7^2)

Finally, we can simplify the square root further:

√147 = 7√3

As you can see, using prime factorization, we have simplified the square root of 147 to 7√3.

Advantages of Prime Factorization

Prime factorization has several advantages when it comes to simplifying square roots. It allows us to break down complex numbers into their simplest form, making it easier to work with. Additionally, prime factorization helps us identify perfect squares, which can be simplified further.

Method 2: Using Square Root Tables

Another way to simplify square roots is by using square root tables. These tables provide a list of square roots for different numbers, making it easier to simplify complex square roots.

For example, let's simplify the square root of 147 using square root tables:

Using a square root table, we find that the square root of 147 is approximately 12.165.

However, we can simplify this further by expressing it as a product of a square root and a whole number:

√147 ≈ 12.165 ≈ 12 + 0.165

Now, we can simplify the square root further:

√147 ≈ 12 + 0.165 ≈ 12 + √0.027

Finally, we can simplify the square root further:

√147 ≈ 12 + √(3^2/100)

As you can see, using square root tables, we have simplified the square root of 147 to an approximate value.

Advantages of Square Root Tables

Square root tables have several advantages when it comes to simplifying square roots. They provide a quick and easy way to find the square root of a number, making it easier to simplify complex square roots. Additionally, square root tables help us identify approximate values, which can be useful in certain calculations.

Conclusion: Simplifying Square Roots Made Easy

In conclusion, simplifying square roots doesn't have to be a daunting task. By using prime factorization and square root tables, we can simplify complex square roots and make them easier to work with. Whether you're a student or a professional, understanding how to simplify square roots can make a significant difference in your calculations.

Take Action: Practice Simplifying Square Roots

Now that you've learned two easy ways to simplify square roots, it's time to practice. Try simplifying the square root of different numbers using prime factorization and square root tables. You can use online resources or practice problems to help you improve your skills.

By practicing simplifying square roots, you'll become more confident in your ability to work with complex numbers and improve your overall math skills.