How do you evalaute \sqrt { 45} \times \sqrt { 64}?

2 Answers
May 5, 2018

24sqrt5

Explanation:

sqrt45 times sqrt64 = sqrt(9*5) times sqrt(8*8) = 3sqrt5 times8 = 24sqrt5

May 5, 2018

24*\sqrt(5)

Explanation:

\sqrt(45)*\sqrt(64)

Write both numbers as a product of prime numbers .
(unique factorization).

45=5*9=5*3*3
64=2*32=2*2*16=2*2*2*8=2*2*2*2*4=
=2*2*2*2*2*2=2^6

\sqrt(45)*\sqrt(64)=

=\sqrt(5*3*3)*\sqrt(2^6)=

=\sqrt(5*3^2)*2^(6/2)=

=\sqrt(5)*\sqrt(3^2)*2^3=

=\sqrt(5)*3*8=

=24*\sqrt(5)