Question

SIMPLIFY: (3+√3) (2+√2)²

Answer 1

Answer:

hope it helps you.

Answer 2

Answer:

The simplified expression for the given problem is: $18+6\sqrt3+4\sqrt6+12\sqrt2$

Step-by-step explanation:

The given expression is: $(3+\sqrt3 )(2+\sqrt2 )^2$

We know that the identity for finding the square of sum of two real numbers or values is as follows:

$(a+b)^2 =a^2 +b^2+2ab$

Using this same identity to simplify the second term of the given expression, we get:

$(3+\sqrt3 )(2+\sqrt2 )^2=(3+\sqrt3)[(2)^2+(\sqrt2)^2+2(2)(\sqrt2)]$

Simplifying further, we get:

$(3+\sqrt3 )(2+\sqrt2 )^2=(3+\sqrt3)[4+2+4\sqrt2]$

$(3+\sqrt3 )(2+\sqrt2 )^2=(3+\sqrt3)[6+4\sqrt2]$

Opening the brackets by multiplying each term of the first bracket with every term of the second bracket, we get:

$(3+\sqrt3 )(2+\sqrt2 )^2=3(6)+(6)\sqrt3+(\sqrt3)4\sqrt2+(3)4\sqrt2$

$(3+\sqrt3 )(2+\sqrt2 )^2=18+6\sqrt3+4\sqrt6+12\sqrt2$

which is the correct answer.