2 Simple Steps To Simplify The Square Root Of 90

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Simplifying square roots can be a daunting task, but with the right approach, it can become a breeze. In this article, we will focus on simplifying the square root of 90, and we will break it down into two simple steps. Whether you are a math enthusiast, a student, or just someone looking to improve your math skills, this article is for you.

The square root of 90 is a value that, when multiplied by itself, gives 90. It's a fundamental concept in mathematics, and being able to simplify it can be useful in various mathematical operations. So, let's dive in and explore the two simple steps to simplify the square root of 90.

Step 1: Break Down the Number 90 into Prime Factors

Before we can simplify the square root of 90, we need to break down the number 90 into its prime factors. Prime factorization is the process of expressing a number as a product of its prime factors. In the case of 90, the prime factorization is:

90 = 2 × 3 × 3 × 5

As you can see, the prime factorization of 90 consists of four prime numbers: 2, 3, 3, and 5.

Step 2: Simplify the Square Root of 90

Now that we have the prime factorization of 90, we can simplify the square root of 90. To do this, we take the square root of each prime factor and multiply them together:

√90 = √(2 × 3 × 3 × 5) = √2 × √3 × √3 × √5 = √(3 × 3) × √2 × √5 = 3√2 × √5 = 3√(2 × 5) = 3√10

And there you have it! The simplified square root of 90 is 3√10.

Benefits of Simplifying Square Roots

Simplifying square roots has several benefits. It can make mathematical operations easier, reduce errors, and improve understanding. In many mathematical contexts, simplifying square roots is essential for obtaining accurate results.

Practical Applications of Simplifying Square Roots

Simplifying square roots has numerous practical applications in various fields, including:

• Mathematics: Simplifying square roots is essential in many mathematical operations, such as solving equations and inequalities.
• Science: Square roots are used in scientific formulas, such as the quadratic formula and the distance formula.
• Engineering: Square roots are used in engineering applications, such as designing electronic circuits and mechanical systems.
• Finance: Square roots are used in finance to calculate interest rates and investment returns.

Common Mistakes to Avoid

When simplifying square roots, there are several common mistakes to avoid:

• Not factoring the number correctly: Make sure to factor the number correctly before simplifying the square root.
• Not simplifying the square root correctly: Make sure to simplify the square root correctly by taking the square root of each prime factor and multiplying them together.
• Not checking the answer: Always check your answer to ensure that it is accurate.

Conclusion

In this article, we have shown that simplifying the square root of 90 can be broken down into two simple steps: breaking down the number 90 into prime factors and simplifying the square root of 90. By following these steps, you can simplify the square root of 90 and improve your math skills. Remember to always check your answer and avoid common mistakes.

We hope that this article has been helpful in simplifying the square root of 90. If you have any questions or comments, please don't hesitate to ask.