Question

What is the following product? (5sqrt4 - 4sqrt3)(5sqrt2 -4sqrt3)

Answer 1

`\boxed{\approx 0,438}`

Explanation:

We have the following product:

`(5√(4) - 4√(3))(5√(2) -4√(3))`

Applying distributive we have the following:

`(5√(4) - 4√(3))(5√(2) -4√(3)) \\ \\ 5 * √(4)√(2)-5* 4√(4)√(3)-4* 5√(3)√(2)+4* 4√(3)√(3)`

By solving the product of square root we have:

`5 *5 √(4)√(2)-5* 4√(4)√(3)-4* 5√(3)√(2)+4* 4√(3)√(3) \\ \\ 25√((4)(2))-20√((4)(3))-20√((3)(2))+16√((3)(3)) \\ \\ 25√(8)-20√(12)-20√(6)+16√(9)`

But
`√(9)=3` then:

`25√(8)-20√(12)-20√(6)+16(3) \\ \\ 25√(8)-20√(12)-20√(6)+48 \approx \boxed{0,438}`