Question

(3√6−2√3)^(2) ........

Answer 1

Відповідь:

54 - 12$\sqrt{18}$ + 12;

54 - 36$\sqrt{2}$ + 12;

66 - 36$\sqrt{2}$ = 15,09.

Answer 2

To simplify the expression $(3\sqrt{6} - 2\sqrt{3})^2$, you can use the formula for squaring a binomial:

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

In this case, $a = 3\sqrt{6}$ and $b = 2\sqrt{3}$. Let's apply the formula:

$(3\sqrt{6} - 2\sqrt{3})^2 = (3\sqrt{6})^2 - 2 \cdot (3\sqrt{6}) \cdot (2\sqrt{3}) + (2\sqrt{3})^2$.

Simplify each term:

$(3\sqrt{6})^2 = 9 \cdot 6 = 54$, $2 \cdot (3\sqrt{6}) \cdot (2\sqrt{3}) = 12\sqrt{18} = 12 \cdot 3\sqrt{2} = 36\sqrt{2}$, $(2\sqrt{3})^2 = 4 \cdot 3 = 12$.

Putting it all together:

$(3\sqrt{6} - 2\sqrt{3})^2 = 54 - 36\sqrt{2} + 12$.

Now combine the constants:

$54 + 12 = 66$.

So, $(3\sqrt{6} - 2\sqrt{3})^2$ simplifies to $66 - 36\sqrt{2}$.