How do you simplify #3/root3(6) #?

3 Answers
Jul 11, 2018

Answer:

#root(3)(9/2)#

Explanation:

we have
#3/root(3)(6)=3/6^(1/3)*3*6^(-1/3)=3*3^(-1/3)*2^ (-1/3)=3^(2/3)/2^(1/3)=root(3)(9/2)#

Answer:

#\root[3]{9/2}#

Explanation:

Given that

#3/\root[3]{6}#

#=\frac{\root[3]{3^3}}{\root[3]{6}}#

#=\root[3]{\frac{3^3}{6}}#

#=\root[3]{27/6}#

#=\root[3]{9/2}#

Jul 11, 2018

Answer:

#3/root(3)(6) = root(3)(36)/2#

Explanation:

To rationalise the denominator, we can proceed as follows:

#3/root(3)(6) = (3 * root(3)(6^2))/(root(3)(6)root(3)(6^2))#

#color(white)(3/root(3)(6)) = (3root(3)(36))/(root(3)(6^3))#

#color(white)(3/root(3)(6)) = (3root(3)(36))/6#

#color(white)(3/root(3)(6)) = root(3)(36)/2#