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# Add. Assume that all variables represent positive real numbers

Add assume that all variables represent positive real numbers

3y√27y+6y√27y3

### 1 Answer by Expert Tutors

William R. | MIT Grad in Physics for Math, Science and More!MIT Grad in Physics for Math, Science an...
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3y√(27y)+6y√(27y3)

First we can simplify the expressions in the radicals to bring out terms.

3y√(9*3*y)+6y√(9*3*y2*y)

The 27 in both radicals have a factor of 9, which is the square of 3. We can bring out this factor by multiplying the terms in front of the radicals by 3. The second term has a factor of y2 which can be pulled out by multiplying the term in front of the radical by y. This gives us

9y√(3y)+18y2√(3y)

Now we can factor out the common term 9y√(3y) from both parts of the expression. This gives our answer

9y√(3y)[1+2y]

We can further simplify this by combining the y and √y in front of the brackets into a single term. y*y1/2=y2/2+1/2=y3/2

Thus, another form of the answer is

9√(3)y3/2[1+2y]