Solve (6sqrt{7}+7sqrt{5})(6sqrt{7}-7sqrt{5})

$$( 6 \sqrt { 7 } + 7 \sqrt { 5 } ) ( 6 \sqrt { 7 } - 7 \sqrt { 5 } )$$

Evaluate

$$7$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(6\sqrt{7}\right)^{2}-\left(7\sqrt{5}\right)^{2}$$

Expand \left(6\sqrt{7}\right)^{2}.

$$6^{2}\left(\sqrt{7}\right)^{2}-\left(7\sqrt{5}\right)^{2}$$

Calculate 6 to the power of 2 and get 36.

$$36\left(\sqrt{7}\right)^{2}-\left(7\sqrt{5}\right)^{2}$$

The square of \sqrt{7} is 7.

$$36\times 7-\left(7\sqrt{5}\right)^{2}$$

Multiply 36 and 7 to get 252.

$$252-\left(7\sqrt{5}\right)^{2}$$

Expand \left(7\sqrt{5}\right)^{2}.

$$252-7^{2}\left(\sqrt{5}\right)^{2}$$

Calculate 7 to the power of 2 and get 49.

$$252-49\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{5} is 5.

$$252-49\times 5$$

Multiply 49 and 5 to get 245.

$$252-245$$

Subtract 245 from 252 to get 7.

$$7$$

Factor

$$7$$