what is sqrt a/b times sqrt a^2/b^2?

Question

please help, i am so confused...

If sqrt a^2/b^2 is a/b and multiply sqrt a/b by a/b i get a sqrt a/ b sqrt b
so now dont i have to multiply the top and bottom by sqrt b to get rid of the radical on the bottom?

Answer 1

Well this might be a little difficult to explain because I certainly can't write this out the way I would on paper. But here it goes.

So first write out the problem, and look for anything that can be simplified. In this case, it will be the [sqrt a^2/b^2] which will be [a / b].

So let's look at our value.
[a / b] x [sqrt. (a / b)].

There are one of two ways you could do this, and according to your question, it appears that you might want to rationalize the denominator (that means there are no sqrts in your denominator). If not, that value above is your answer.

If you do want to rationalize:
Multiply the second term [sqrt. (a / b)] by [sqrt. b / sqrt. b] (and this is okay to do because sqrt. b / sqrt. b is basically 1) Now your term should look like: [(sqrt. ab) / b].

Back to the entire problem: so
[a / b] x [(sqrt. ab) / b] = [ (a sqrt. ab) / b^2]

This would look a lot cleaner on paper when you don't have to write everything in a line and use sqrt instead of the actual notation. Hoped this helped.

Answer 2

This can be solved by substitution.
Given : 1. (sqrt (a/b)) * (sqrt ((a^2)/(b^2)))
First notice that a^2 = a*a and b^2 = b*b, and substitute.
2. (sqrt (a/b)) * (sqrt ((a*a)/(b*b)))
The fraction (a*a)/(b*b) can have it's numerators and denominators rearanged and still have the same value.
3. (sqrt (a/b)) * (sqrt ((a/b) * (a/b)))
Here you have a value, a/b, multiplied by itself, hense it is squared.
4. (sqrt (a/b)) * (sqrt ((a/b)^2))
Here you have the square root of a value that is squared, that is the same as the original value. (Technically it is the absolute value, but I am assuming you are not dealing with negative numbers here.)
5. (sqrt (a/b)) * (a/b)
The square root is the same as raising the value to the 1/2 power. The value standing by itself is the same as being raised to the 1th power.
6. ((a/b)^0.5) * ((a/b)^1.0)
Here you have a value, a/b, raised to a power multiplied by the same value raised to a power. By the theory of logarithms you can multiply values raised to powers by adding their powers.
7. (a/b)^(0.5+1.0)
8. (a/b)^1.5
This is the simplest expression of the original given.

Answer 3

Don't be confused, be happy. The second term is (a/b) in disguise. So multiply the terms together to get
(a/b) sqrt (a/b)

Answer 4

ok to start with sqrt a^2/b^2 is just a/b so it's (a/b)^.5 times a/b or just (a/b)^1.5