Simplifying Radical Expressions: Proving 20/6√24 5/3√6

Understanding and simplifying radical expressions is a fundamental skill in algebra. In this article, we will walk through the process of proving the equation 20/6√24 5/3√6.

Step-by-Step Explanation

We start with the left-hand side of the equation (LHS): 20/6√24.

First, simplify the radicand:

LHS 20/6√24 20/6√(22×3) 20/6√23×6

Divide the coefficient by 6:

LHS 20/6√23×6 10/3×√23×6 10/3√62

Further simplify the expression:

LHS 10/3√62 10/3×2√6 20/6√6 5/3√6

This step-by-step process proves that the left-hand side (LHS) equals the right-hand side (RHS) of the equation, i.e., 20/6√24 5/3√6.

Another Method

To prove the equation using an alternative method, follow these steps:

Start with the left-hand side (LHS) again:

LHS 20/6√24

Express 24 as 4×6:

LHS 20/6√24 20/6√(4×6)

Separate the square root into two parts:

LHS 20/6√4×6 20/6√4×√6 20/6×2√6 20×2/6√6 40/6√6 20/3√6

Simplify the fraction:

LHS 20/3√6 (20/3)÷(6/3)√6 20/6√6 5/3√6

Therefore, using an alternative approach, we also arrive at the conclusion that LHS RHS i.e., 20/6√24 5/3√6.

Aids and Applications

Understanding radical expressions and the methods to simplify them is crucial in various fields including engineering, physics, and mathematics. The ability to manipulate and simplify expressions like this helps in solving more complex problems efficiently.

Conclusion

The proof that 20/6√24 5/3√6 is a classic example of manipulating radical expressions. By understanding and practicing these techniques, you can enhance your algebraic and problem-solving skills. Let's continue to explore more advanced topics in algebra and algebraic expressions.