Video Transcript
Simplify negative 11 over 18 times the square root of two by rationalizing the denominator.
In this question, we are given an expression involving a radical in the denominator. And we are asked to simplify the expression by rationalizing the denominator. This means that we want to find an equivalent value with a positive integer in the denominator.
We can rewrite fractions into an equivalent form by multiplying the numerator and denominator by the same nonzero value. We note that there is a factor of root two in the denominator. So, we can multiply this by root two in order to obtain an integer. This gives us negative 11 times the square root of two over 18 times the square root of two times the square root of two.
We can simplify the product in the denominator by recalling that if 𝑎 is nonnegative, then root 𝑎 times root 𝑎 is equal to 𝑎. This gives us negative 11 root two over 18 times two. Evaluating the product in the denominator gives us negative 11 root two over 36. The denominator is a positive integer, and we cannot cancel any shared factors. So, we cannot simplify the expression any further.
