Please help me figure out the steps to solving this problem?
#4/sqrt2+2/sqrt3#
1 Answer
Explanation:
The first thing that you need to do here is to get rid of the two radical terms from the denominators.
To do that, you must rationalize the denominator by multiplying each radical term by itself.
So what you do is you take the first fraction and multiply it by
#4/sqrt(2) * sqrt(2)/sqrt(2) = (4 * sqrt(2))/(sqrt(2) * sqrt(2))#
Since you know that
#sqrt(2) * sqrt(2) = sqrt(2 * 2) = sqrt(4) = sqrt(2^2) = 2#
you can rewrite the fraction like this
#(4 * sqrt(2))/(sqrt(2) * sqrt(2)) = (4 * sqrt(2))/2 = 2sqrt(2)#
Now do the same for the second fraction, only this time, multiply it by
#2/sqrt(3) * sqrt(3)/sqrt(3) = (2 * sqrt(3))/(sqrt(3) * sqrt(3))#
Since
#sqrt(3) * sqrt(3) = sqrt(3^2) = 3#
you will have
#(2 * sqrt(3))/(sqrt(3) * sqrt(3)) = (2 * sqrt(3))/3#
This means that the original expression is now equivalent to
#4/sqrt(2) + 2/sqrt(3) = 2sqrt(2) + (2sqrt(3))/3#
Next, multiply the first term by
#2sqrt(2) * 3/3 + (2sqrt(3))/3 = (6sqrt(2))/3 + (2sqrt(3))/3#
The two fractions have the same denominator, so you can add their numerators to get
#(6sqrt(2))/3 + (2sqrt(3))/3 = (6sqrt(2) + 2sqrt(3))/3#
Finally, you can use
#(6sqrt(2) + 2sqrt(3))/3 = (2(3sqrt(2) + sqrt(3)))/3#
And there you have it
#4/sqrt(2) + 2/sqrt(3) = (2(3sqrt(2) + sqrt(3)))/3#