Add. Assume that all variables represent positive real numbers

Question

Add assume that all variables represent positive real numbers 

 

3y√27y+6y√27y³

Answer 1

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*y^1/2=y^2/2+1/2=y^3/2

 

Thus, another form of the answer is

 

9√(3)y^3/2[1+2y]