Question

I need help solving this radical equation with box or foil method​

Answer 1

`(3√(3) -2√(2))^2=35-12√(6)`

Explanation:

Using the FOIL method:

`F+O+I+L`

Simplify the expression by squaring:

`(3√(3)-2√(2) )(3√(3)-2√(2))`

Now we can use the Foil method:

First, Outside, Inside, Last

Multiply the first terms within each grouping:

`3√(3)*3√(3) \\\\3*3√(3*3) \\\\9√(9) \\\\9*3\\\\27`

Insert as the first term:

`27+O+I+L`

Now multiply the outside terms in each grouping:

`3√(3) *(-2√(2))\\\\-3*2√(3*2) \\\\-6√(6)`

Insert as the next term:

`27-6√(6) +I+L`

Now multiply the inside terms:

`-2√(2) *3√(3) \\\\-2*3√(2*3) \\\\-6√(6)`

Insert as the third term:

`27-6√(6) -6√(6)+L`

Now multiply the last terms in the grouping:

`-2√(2) *(-2√(2) )\\\\-2*(-2)√(2*2)\\\\ 4√(4)\\\\4*2\\\\8`

Insert as the last term:

`27-6√(6) -6√(6)+8`

Simplify by combining like terms:

`27+8-6√(6) -6√(6)\\\\35-12√(6)`

:Done