Question

Simplify √10 · √6
1. √18
2. 4√5
3. √80
4. 8√10

Answer 1

Explanation:

so there are square root properties that they want you to recognize and respect :P everyone wants a little respect, even the square root sign :D

first we can move things under one root sign, like this...

`√(10)` *
`√(6)` =
`√(10 * 6)`

now we can do that multiplication under the square root sign.

`√(10 * 6)` =
`√(60)`

now we can think about this for a long long time and see that 60 can be split up in other ways besides 10 * 6

for instance 15 * 4 also is 60

so this is equal
`√(15 * 4)` =
`√(10 * 6)` =
`√(60)`

now just take out the perfect square part

2 *
`√(15)`

this isn't one of the listed answers but it is a correct answer , for what is being asked. The teacher got the question wrong :o