How do you evaluate #(2\sqrt { 2} + 5) ( \sqrt { 10} - 3)#?

1 Answer
Jan 30, 2018

Approximately #1.2704#

Explanation:

Now, remember that:
#(a+b)(c+d)=ac+ad+bc+bd#

Therefore, #(2sqrt2+5)(sqrt10-3)# is equal to #2sqrt2*sqrt10+(-3*2sqrt2)+5sqrt10-15# Now, remember that: #sqrta*sqrtb=sqrt(ab)#

Therefore, we can simplify #2sqrt2*sqrt10+(-3*2sqrt2)+5sqrt10-15#.

=>#2sqrt2*sqrt10+(-3*2sqrt2)+5sqrt10-15#

=>#2sqrt20-6sqrt2+5sqrt10-15# Now, remember that: #sqrt (a^2*b)=asqrtb#

=>#4sqrt5-6sqrt2+5sqrt10-15#

=>#-6sqrt2+4sqrt5+5sqrt10-15# which is approximately #1.2704#