Solve (2sqrt{3}+8sqrt{7})(sqrt{3}+8sqrt{7})

$$( 2 \sqrt { 3 } + 8 \sqrt { 7 } ) ( \sqrt { 3 } + 8 \sqrt { 7 } )$$

Evaluate

$$24\sqrt{21}+454\approx 563.981816679$$

Solution Steps

Apply the distributive property by multiplying each term of 2\sqrt{3}+8\sqrt{7} by each term of \sqrt{3}+8\sqrt{7}.

$$2\left(\sqrt{3}\right)^{2}+16\sqrt{3}\sqrt{7}+8\sqrt{7}\sqrt{3}+64\left(\sqrt{7}\right)^{2}$$

The square of \sqrt{3} is 3.

$$2\times 3+16\sqrt{3}\sqrt{7}+8\sqrt{7}\sqrt{3}+64\left(\sqrt{7}\right)^{2}$$

Multiply 2 and 3 to get 6.

$$6+16\sqrt{3}\sqrt{7}+8\sqrt{7}\sqrt{3}+64\left(\sqrt{7}\right)^{2}$$

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

$$6+16\sqrt{21}+8\sqrt{7}\sqrt{3}+64\left(\sqrt{7}\right)^{2}$$

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

$$6+16\sqrt{21}+8\sqrt{21}+64\left(\sqrt{7}\right)^{2}$$

Combine 16\sqrt{21} and 8\sqrt{21} to get 24\sqrt{21}.

$$6+24\sqrt{21}+64\left(\sqrt{7}\right)^{2}$$

The square of \sqrt{7} is 7.

$$6+24\sqrt{21}+64\times 7$$

Multiply 64 and 7 to get 448.

$$6+24\sqrt{21}+448$$

Add 6 and 448 to get 454.

$$454+24\sqrt{21}$$

Factor

$$2 {(12 \sqrt{21} + 227)} = 563.981816679$$