How do you multiply and simplify by factoring #sqrt10*sqrt35#?

1 Answer
Jan 11, 2017

Answer:

#5sqrt(14)#

Explanation:

Introductory note: #sqrt(axxb) " is the same as "sqrt(a)xxsqrt(b)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Given:#" "sqrt10" "xx" "sqrt35#

Write as: #" "sqrt(2xx5)" "xx" "sqrt(5xx7)#

Which is also the same as:#" "sqrt2xxsqrt5xxsqrt5xxsqrt7#

But #sqrt5xxsqrt5 = 5# giving:#" "5sqrt2xxsqrt7#

but this is the same as:#" "5sqrt(2xx7)" "=" "5sqrt(14)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check:

#" "5sqrt(14) ~~18.70828......#

#sqrt(10)xxsqrt(35) ~~ 18.70828......#