Rationalising the denominator. 15/sqrt[3]

[hemmed]

Hi there,

I need to rationalise the following denominator:

\(\displaystyle {\large\frac{15}{\sqrt{3}}}\)

And the answer given is

\(\displaystyle {\large5\sqrt{3}}\)

However I'm struggling to get to this, I get to here, basically:

\(\displaystyle {\large\frac{5\sqrt[2]{3^2}}{3}}\)

Or \(\displaystyle {\large{\frac{\sqrt{5}\sqrt[2]{3^2}}{3}}}\)

On the first instance (\(\displaystyle {\large\frac{5\sqrt[2]{3^2}}{3}}\)) do I just need to cancel out the 3s, leaving me with \(\displaystyle {\large5\sqrt{3}}\)?

 

[ksdhart2]

So, there's two main ways you could solve this problem, and it looks to me like you've tried to do a bit of both and as a result ended up with a jumbled, confusing mess. The first method involves factoring the numerator. This won't always work for problems of this type, but it will for this specific one:

\(\displaystyle \dfrac{15}{\sqrt{3}}=\dfrac{5 \cdot 3}{\sqrt{3}}=\dfrac{5 \cdot \sqrt{3} \cdot \sqrt{3}}{\sqrt{3}}\)

The second method, which works for any "rationalize the denominator" problem is to do just that.

\(\displaystyle \dfrac{15}{\sqrt{3}}=\dfrac{15}{\sqrt{3}} \cdot \dfrac{\sqrt{3}}{\sqrt{3}}=\dfrac{15 \cdot \sqrt{3}}{3}\)

 

[hemmed]

So, there's two main ways you could solve this problem, and it looks to me like you've tried to do a bit of both and as a result ended up with a jumbled, confusing mess. The first method involves factoring the numerator. This won't always work for problems of this type, but it will for this specific one:

\(\displaystyle \dfrac{15}{\sqrt{3}}=\dfrac{5 \cdot 3}{\sqrt{3}}=\dfrac{5 \cdot \sqrt{3} \cdot \sqrt{3}}{\sqrt{3}}\)

The second method, which works for any "rationalize the denominator" problem is to do just that.

\(\displaystyle \dfrac{15}{\sqrt{3}}=\dfrac{15}{\sqrt{3}} \cdot \dfrac{\sqrt{3}}{\sqrt{3}}=\dfrac{15 \cdot \sqrt{3}}{3}\)

Yup I was being an idiot!


\(\displaystyle \dfrac{15}{\sqrt{3}}=\dfrac{15}{\sqrt{3}} \cdot \dfrac{\sqrt{3}}{\sqrt{3}}=\dfrac{15 \cdot \sqrt{3}}{3}\)

And then obviously you can reduce 15/3 to 5/1. Thank you for your help