Question

What is the product of three square root of eight times four square root of three? Simplify your answer.

Answer 1

`The\ product\ of 3 √(8)*4 √(3)\ is\ 24 √(6).`


First, recognize that all the numbers can be moved around because they are being multiplied together.
Next, rearrange the expression so that the whole-number coefficients are together:


`3√(8)*4√(6)`

`3*4*√(8)*√(3)`

Now try to simplify the square-roots to find any squares inside that can be reduced and taken out of the square-root:


`3*4*√((2*2*2))*√(3)`

`3*4*√(4*2)*√(3)`

Multiply the square roots together:

`3*4*√((4*2*3))`

`3*4*√((4*6))`

Now take out the square-root of 4 and simplify

`3*4*√(4)*√(6)`

`3*4*(2)*√(6)`

`24√(6)`


`Thus,\ your\ answer\ is\ 24√(6)`