2 Ways To Simplify Square Root Of 72

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Simplifying the square root of 72 can seem daunting at first, but with a few simple steps, you can break it down into a more manageable expression. In this article, we will explore two methods to simplify the square root of 72.

Method 1: Prime Factorization

The first method involves prime factorization, which is a technique used to break down a number into its prime factors. To simplify the square root of 72, we start by finding the prime factors of 72.

72 = 2 × 2 × 2 × 3 × 3

Now, we can group the prime factors into pairs:

(2 × 2) × (2 × 3 × 3)

Next, we take the square root of each pair:

√(2 × 2) × √(2 × 3 × 3)

Simplifying further, we get:

2√(2 × 3 × 3)

Finally, we can simplify the expression by combining the remaining prime factors:

2√(6 × 6)

So, the simplified square root of 72 is:

2√36

What is the Significance of Prime Factorization?

Prime factorization is a powerful technique that helps us break down complex numbers into their simplest form. By finding the prime factors of a number, we can identify patterns and relationships that may not be immediately apparent. In the case of simplifying the square root of 72, prime factorization allows us to group the prime factors into pairs, making it easier to take the square root.

Method 2: Finding Perfect Squares

The second method involves finding perfect squares that can be factored out of the expression. To simplify the square root of 72, we can start by looking for perfect squares that divide into 72.

72 = 36 × 2

Since 36 is a perfect square (6 × 6), we can take the square root of 36:

√36 = 6

Now, we can rewrite the expression as:

√(36 × 2)

Simplifying further, we get:

6√2

So, the simplified square root of 72 is:

6√2

What are the Benefits of Finding Perfect Squares?

Finding perfect squares is a useful technique that can help simplify complex expressions. By identifying perfect squares that divide into a number, we can break down the expression into more manageable parts. In the case of simplifying the square root of 72, finding perfect squares allows us to take the square root of 36, making it easier to simplify the expression.

Comparison of Methods

Both methods are effective in simplifying the square root of 72, but they differ in their approach. Prime factorization involves breaking down the number into its prime factors, while finding perfect squares involves identifying perfect squares that divide into the number.

Method 1: Prime Factorization

• Involves breaking down the number into its prime factors
• Can be more time-consuming, but provides a deeper understanding of the number's structure
• Results in the expression 2√36

Method 2: Finding Perfect Squares

• Involves identifying perfect squares that divide into the number
• Can be faster and more straightforward, but may not provide the same level of insight into the number's structure
• Results in the expression 6√2

Conclusion: Simplifying the Square Root of 72

Simplifying the square root of 72 can seem daunting, but with the right techniques, it can be broken down into a more manageable expression. By using prime factorization or finding perfect squares, we can simplify the square root of 72 into two different expressions: 2√36 and 6√2. Both methods have their benefits and drawbacks, and the choice of method depends on the individual's preference and the specific problem.

Takeaways

• Prime factorization involves breaking down a number into its prime factors
• Finding perfect squares involves identifying perfect squares that divide into a number
• Both methods can be used to simplify the square root of 72
• The choice of method depends on the individual's preference and the specific problem

We hope this article has provided you with a deeper understanding of how to simplify the square root of 72. Whether you prefer prime factorization or finding perfect squares, both methods can help you break down complex expressions into more manageable parts.