Write a factor that you can use to rationalize the denominator of $\frac{4}{\sqrt{6}}$.
A rationalizing factor is $\square$.
Answer (1)
Identify the denominator as 6 .
Multiply the numerator and denominator by 6 to rationalize the denominator.
Simplify the expression: 6 4 × 6 6 = 6 4 6 = 3 2 6 .
The rationalizing factor is 6 .
Explanation
Understanding the Problem We are given the expression 6 4 and we want to find a factor that will rationalize the denominator.
Identifying the Rationalizing Factor The denominator is 6 . To rationalize the denominator, we need to multiply both the numerator and the denominator by a factor that will eliminate the square root in the denominator.
Rationalizing the Denominator In this case, we can multiply the numerator and denominator by 6 : 6 4 × 6 6 = 6 4 6 = 3 2 6 The denominator is now rational.
Final Answer Therefore, the rationalizing factor is 6 .
Examples
Rationalizing the denominator is a useful skill when simplifying expressions or solving equations involving radicals. For example, in physics, you might encounter an expression with a square root in the denominator when calculating the velocity of an object. Rationalizing the denominator can make it easier to work with the expression and obtain a more accurate result. Suppose you have an expression like 2 5 . Rationalizing the denominator gives you 2 5 2 , which is often easier to use in further calculations.
