Video Transcript
Which of the following is equal to
four times the square root of six to the negative one power? A) 24, B) two-thirds, C) four times
the square root of six, or D) two times the square root of six over three.
We’re given four times the square
root of six to the negative one power. First, we should remember that 𝑥
to the negative 𝑎 power is equal to one over 𝑥 to the 𝑎 power. And this means we could rewrite
four times the square root of six to the negative one power as four over the square
root of six. But none of our answer choices look
like this.
So the next thing we want to do is
see if we can get the square root of six out of the denominator. One way to do that is by
multiplying this fraction by the square root of six over the square root of six. We know that the value of the
square root of six over the square root of six is one. And so we’re not changing the value
of this fraction. We’re simply rewriting it. And this process is called
rationalising. We’re rationalising the denominator
here.
To multiply these fractions, we
multiply their numerators, which is four times the square root of six. And in the denominator, we would
have the square root of six times the square root of six, which equal six. Four times the square root of six
over six is equal to the expression we started with.
But now we notice that we have a
numerator and a denominator that’s divisible by two. Four divided by two is two. And six divided by two is
three. Which means we can simplify four
times the square root of six over six to say two times the square root of six over
three, which is option D.
