Please help me figure out the steps to solving this problem?

#4/sqrt2+2/sqrt3#

Answer 1

#(2(3sqrt(2) + sqrt(3)))/3#

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 #1 = sqrt(2)/sqrt(2)# in order to keep its value the same. This will get you
#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 #1 = sqrt(3)/sqrt(3)#. You will get
#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 #1 = 3/3# to get
#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 #2# as a common factor here to rewrite the fraction as
#(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#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7