Rationalise the denominator of the following expression. That is, find an equivalent expression that does not have a square root in the denominator.Tip: Remember it can often be useful to multiply a fraction by 1. Why do we choose to multiply by 5−6‾√5−6‾√?15+6‾√=15+6‾√×5−6‾√5−6‾√=
Question
Rationalise the denominator of the following expression. That is, find an equivalent expression that does not have a square root in the denominator.Tip: Remember it can often be useful to multiply a fraction by 1. Why do we choose to multiply by 5−6‾√5−6‾√?15+6‾√=15+6‾√×5−6‾√5−6‾√=
Solution
The expression you provided seems to be incomplete or incorrectly formatted. However, I can explain the process of rationalizing the denominator using a similar example.
Let's take the expression (15 + sqrt(6)) / (5 - sqrt(6)).
Step 1: Multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of (5 - sqrt(6)) is (5 + sqrt(6)).
So, (15 + sqrt(6)) / (5 - sqrt(6)) * (5 + sqrt(6)) / (5 + sqrt(6))
Step 2: Apply the difference of squares formula in the denominator, which is (a - b)(a + b) = a^2 - b^2.
So, ((15 + sqrt(6)) * (5 + sqrt(6))) / ((5)^2 - (sqrt(6))^2)
Step 3: Simplify the expression.
This is the general process of rationalizing the denominator. If you provide a correctly formatted expression, I can help you solve it.
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