Question

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

Answer 1

Answer:

$(3\sqrt{3} -2\sqrt{2})^2=35-12\sqrt{6}$

Step-by-step explanation:

Using the FOIL method:

$F+O+I+L$

Simplify the expression by squaring:

$(3\sqrt{3}-2\sqrt{2} )(3\sqrt{3}-2\sqrt{2})$

Now we can use the Foil method:

First, Outside, Inside, Last

Multiply the first terms within each grouping:

$3\sqrt{3}*3\sqrt{3} \\\\3*3\sqrt{3*3} \\\\9\sqrt{9} \\\\9*3\\\\27$

Insert as the first term:

$27+O+I+L$

Now multiply the outside terms in each grouping:

$3\sqrt{3} *(-2\sqrt{2})\\\\-3*2\sqrt{3*2} \\\\-6\sqrt{6}$

Insert as the next term:

$27-6\sqrt{6} +I+L$

Now multiply the inside terms:

$-2\sqrt{2} *3\sqrt{3} \\\\-2*3\sqrt{2*3} \\\\-6\sqrt{6}$

Insert as the third term:

$27-6\sqrt{6} -6\sqrt{6}+L$

Now multiply the last terms in the grouping:

$-2\sqrt{2} *(-2\sqrt{2} )\\\\-2*(-2)\sqrt{2*2}\\\\ 4\sqrt{4}\\\\4*2\\\\8$

Insert as the last term:

$27-6\sqrt{6} -6\sqrt{6}+8$

Simplify by combining like terms:

$27+8-6\sqrt{6} -6\sqrt{6}\\\\35-12\sqrt{6}$

:Done