How do you simplify #(3+root3(3))/(root3(9))#?

Question

Genesis Allen · Accepted Answer

#(3+root(3)3)/root(3)9=root(3)3+root(3)9/3# Simplifying #(3+root(3)3)/root(3)9# means rationalizing the denominator i.e. converting irrational denominator to a rational denominator, As denominator is #root(3)9=root(3)(3xx3)#, to convert it into a rational number, we need to take everything outside the cube root sign. However, we could have done so only if we had three #3#'s, but we have only two #3#'s. Hence, we need to multiply denominator by #root(3)3#, but to keep the expression same, we will have to multiply numerator too by #root(3)3#. Hence #(3+root(3)3)/root(3)9# = #(3+root(3)3)/root(3)9xxroot(3)3/root(3)3# = #(3root(3)3+root(3)3xxroot(3)3)/root(3)27# = #(3root(3)3+root(3)9)/3# = #root(3)3+root(3)9/3#

Savannah Anderson · Answer

undefined To simplify the expression (3+√3(3))/(√3(9)), we can start by simplifying the denominator. √3(9) simplifies to √3 * 3, which is equal to 3√3.

Now, let's simplify the numerator. √3(3) simplifies to 3√3.

So, the expression becomes (3+3√3)/(3√3).

To simplify further, we can factor out a common term from the numerator. The common term is 3.

Thus, the expression simplifies to 3(1+√3)/(3√3).

Next, we can cancel out the common factor of 3 between the numerator and denominator.

This leaves us with (1+√3)/(√3).

And that is the simplified form of the expression (3+√3(3))/(√3(9)).