Question

What is the simplified form of ( square root of 140)?

Answer 1

So,


`√(140)`

Remember that we can multiply the radicands if the indices are the same. We can do the opposite thing by breaking 140 into smaller numbers in order to find perfect squares.


`√(140) --\ \textgreater \ √(4) * √(35)`

Simplify.

`2 √(35)`

There are no more perfect squares to be found, so therefore the radical is simplified.

Answer 2

If you do a factor tree (I did it on paper), you will find that 140 can be expressed as 2*2*5*7. Since we have two twos, we can factor them out of the radical as
`√(4)`, which is equal to 2. It looks like this:


`√(140)`

into


`√(4)* √(35)`

Changing \sqrt{4} to 2, we get the simplified result:


`2 √(35)`

And that is as simple as you can go.

Hope that helped!

~Cam943