Answer:
[tex] \displaystyle x = 2 \sqrt{3} [/tex]
Step-by-step explanation:
we would like to solve the following equation:
[tex] \displaystyle \sqrt{3} = \frac{6}{x} [/tex]
in order to do so do cross multiplication:
[tex] \displaystyle x \sqrt{3} = 6[/tex]
divide both sides by √3:
[tex] \displaystyle x = \frac{6}{ \sqrt{3}} [/tex]
since we ended up with a square root on the denominator so we can consider rationalising the denominator to do so multiply both numerator and denominator by √3 which yields:
[tex] \displaystyle x = \frac{6}{ \sqrt{3}} \times \frac{ \sqrt{3} }{ \sqrt{ 3} } [/tex]
simplify multiplication:
[tex] \displaystyle x = \frac{6 \sqrt{3} }{ 3} [/tex]
reduce fraction:
[tex] \displaystyle x = 2 \sqrt{3} [/tex]
and we are done!
