Question

How do you simplify `sqrt12*sqrt10`?

Answer 1

`=sqrt(2^2*3)sqrt10=2sqrt3*sqrt10=2sqrt30`

Answer 2

Very slightly different presentation
`2sqrt(30)`

Explanation:

Look for common values that are in both roots. If we can find values that end being squared we can 'take them outside' the square roots.

Given:`" "sqrt(12)sqrt(10)`

Whole number factors of 12 are:
{1,12}, {2,6}, {3,4}`" "` Note that {3,4}`->{3, 2^2}`

Whole number factors of 10 are:
{1, 10}, {2,5}
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I can not spot any other possible useful combination than the following.

Write as:`" "sqrt(3xx2^2)xxsqrt(10)`

`2sqrt(3)xxsqrt(10)`

`2sqrt(3xx10)`

`color(blue)(=2sqrt(30))`