7 Ways To Simplify Radical Expression Of 7/108

Radical expressions, particularly when involving fractions, can appear complex at first glance. However, simplifying these expressions can make them more manageable and easier to work with. In this article, we will explore 7 ways to simplify the radical expression of 7/108, breaking down the process into clear steps to help you grasp the concept effectively. By following these methods, you will gain a better understanding of simplifying radicals and be able to apply these techniques to similar mathematical problems.

Understanding Radical Expressions

Before delving into the simplification of the radical expression 7/108, it is essential to understand the basics of radical expressions. In mathematics, radicals are expressions containing roots, such as square roots (√) or cube roots (³√). Rationalizing the denominator involves removing radicals from the denominator or simplifying them to rational numbers, facilitating easier computations and a clearer representation of the mathematical expression.

<div style="text-align: center;"> <img src="https://tse1.mm.bing.net/th?q=radical expressions" alt="Radical Expressions"> </div>

7 Ways to Simplify the Radical Expression of 7/108

1. Identify the Square Root: The radical expression of 7/108 can be simplified by finding the square root of the denominator, 108, which is 2 x 2 x 3 x 3 x 3.

2. Express in Prime Factorization: Rewrite 108 in its prime factorization form, 2² * 3³, to easily identify perfect squares.

3. Reduce the Fraction: Divide both the numerator (7) and denominator (108) by their greatest common factor (GCF) to simplify the fraction.

4. Simplify the Square Root: Express the square root of 108 as the square root of 36 (2² * 3²) multiplied by the square root of 3.

5. Combine Like Terms: Simplify the square root of 36, resulting in 6, and leave the square root of 3 outside the square root symbol.

6. Final Expression: Combine the simplified fraction (7/108) with the radical expression, resulting in 7√3 / 6.

7. Rationalize the Denominator (Optional): To further simplify the expression, multiply both the numerator and the denominator by the conjugate of the denominator to eliminate the radical from the denominator.

By following these 7 steps, you can effectively simplify the radical expression of 7/108, gaining a better grasp of radical expressions and fraction simplification in mathematics.

For any further clarification or practice exercises on simplifying radical expressions, feel free to explore additional resources or seek guidance from a mathematics tutor.

FAQ Section

<div class="faq-section"> <div class="faq-container"> <div class="faq-item"> <div class="faq-question"> <h3>What is a radical expression?</h3> <span class="faq-toggle">+</span> </div> <div class="faq-answer"> <p>A radical expression is an algebraic expression that includes a radical symbol (√), indicating a root of a number or variable.</p> </div> </div> <div class="faq-item"> <div class="faq-question"> <h3>How can I simplify radical expressions?</h3> <span class="faq-toggle">+</span> </div> <div class="faq-answer"> <p>To simplify radical expressions, identify perfect squares, factorize radicals, and rationalize denominators when necessary.</p> </div> </div> <div class="faq-item"> <div class="faq-question"> <h3>Why is simplifying radicals important?</h3> <span class="faq-toggle">+</span> </div> <div class="faq-answer"> <p>Simplifying radicals makes mathematical expressions easier to work with, reduces complexity, and aids in clearer understanding of the problem.</p> </div> </div> </div> </div>