Question

Can someone please help me with a problem, I am not to sure how to do it. I need to simplify the expression and my answer should be in simplified radical form. The expression is √20/7

Answer 1

is it this \[\sqrt20/7 \] where the sqrt only covers the 20
or this \[\sqrt(20/7)\]
where the sqrt is over the whole thing?

Answer 2

@ijakez It covers the entire fraction

Answer 3

Taking the entire radical-with-fraction:\[\sqrt{\frac{ 20 }{ 7 }}\] ... we have two goals. The first is to recognize that 20 can be factored, and to factor it so that one factor is a perfect square. The second is to get that 7 out from under the radical, since we don't want our final answer to have a radical in the denominator. Any ideas of what to do first?

Answer 4

@mathmale I don't know if this is correct but from what I was taught to do was that you can't leave a radical as a denominator, and you have to rationalize the denominator and multiply the denominator and numerator

Answer 5

That's one step you have to do, you can multiply both the top and bottom by rad7 in order to rationalize it. However, it's equally important to find if there is any perfect square you can factor out of 20.
If the problem was just \[\sqrt20\], how would you simplify it?

Answer 6

@ijakez Is the answer 2 √25/7 ?

Answer 7

Nope! Just break it up part by part. Simplify \[\sqrt20\] first

Answer 8

@ijakez Never mind, I'll just handle this on my own

Answer 9

I can try to help!
You have to simplify sqrt of 20, and you break it up like this
circling any perfect square or number that can't be broken up further.
4 is a perfect square, the sqrt of 4 is 2, so sqrt of 20 can be simplified to \[2 \sqrt5\]
Now, you have to rationalize the expression by multiplying it by \[\sqrt7/\sqrt7\]. You end up with \[2\sqrt35/7\]