Evaluate (2 square root of 6)^2-3( square root of 21)^2

${(2 \sqrt{6})}^{2} - 3 {(\sqrt{21})}^{2}$

Simplify each term.

Apply the product rule to $2 \sqrt{6}$ .

$2^{2} {\sqrt{6}}^{2} - 3 {(\sqrt{21})}^{2}$

Raise $2$ to the power of $2$ .

$4 {\sqrt{6}}^{2} - 3 {(\sqrt{21})}^{2}$

Rewrite ${\sqrt{6}}^{2}$ as $6$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ .

$4 {(6^{\frac{1}{2}})}^{2} - 3 {(\sqrt{21})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$4 \cdot 6^{\frac{1}{2} \cdot 2} - 3 {(\sqrt{21})}^{2}$

Combine $\frac{1}{2}$ and $2$ .

$4 \cdot 6^{\frac{2}{2}} - 3 {(\sqrt{21})}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 \cdot 6^{\frac{2}{2}} - 3 {(\sqrt{21})}^{2}$

Rewrite the expression.

$4 \cdot 6^{1} - 3 {(\sqrt{21})}^{2}$

Evaluate the exponent.

$4 \cdot 6 - 3 {(\sqrt{21})}^{2}$

Multiply $4$ by $6$ .

$24 - 3 {(\sqrt{21})}^{2}$

Rewrite ${\sqrt{21}}^{2}$ as $21$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{21}$ as $21^{\frac{1}{2}}$ .

$24 - 3 {(21^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$24 - 3 \cdot 21^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$24 - 3 \cdot 21^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$24 - 3 \cdot 21^{\frac{2}{2}}$

Rewrite the expression.

$24 - 3 \cdot 21^{1}$

Evaluate the exponent.

$24 - 3 \cdot 21$

Multiply $- 3$ by $21$ .

$24 - 63$

Subtract $63$ from $24$ .

$- 39$