How do you simplify sqrt12*sqrt10?

2 Answers
P dilip_k
Apr 22, 2016

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

Tony B
Apr 22, 2016

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))

Related questions
See all questions in Multiplication and Division of Radicals
Impact of this question
1165 views around the world
You can reuse this answer
Creative Commons License