Solve -24*sqrt{7}*sqrt{3}+3(4*sqrt{7}*sqrt{3})^2

$$- 24 \cdot \sqrt { 7 } \cdot \sqrt { 3 } + 3 ( 4 \cdot \sqrt { 7 } \cdot \sqrt { 3 } ) ^ { 2 }$$

Evaluate

$$1008-24\sqrt{21}\approx 898.018183321$$

Solution Steps

To multiply \sqrt{7} and \sqrt{3}, multiply the numbers under the square root.

$$-24\sqrt{21}+3\times \left(4\sqrt{7}\sqrt{3}\right)^{2}$$

To multiply \sqrt{7} and \sqrt{3}, multiply the numbers under the square root.

$$-24\sqrt{21}+3\times \left(4\sqrt{21}\right)^{2}$$

Expand \left(4\sqrt{21}\right)^{2}.

$$-24\sqrt{21}+3\times 4^{2}\left(\sqrt{21}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$-24\sqrt{21}+3\times 16\left(\sqrt{21}\right)^{2}$$

The square of \sqrt{21} is 21.

$$-24\sqrt{21}+3\times 16\times 21$$

Multiply 16 and 21 to get 336.

$$-24\sqrt{21}+3\times 336$$

Multiply 3 and 336 to get 1008.

$$-24\sqrt{21}+1008$$

Factor

$$24 {(42 - \sqrt{21})} = 898.018183321$$