Solve (10+3sqrt{7})(10-3sqrt{7})

$$( 10 + 3 \sqrt { 7 } ) ( 10 - 3 \sqrt { 7 } )$$

Evaluate

$$37$$

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}.

$$10^{2}-\left(3\sqrt{7}\right)^{2}$$

Calculate 10 to the power of 2 and get 100.

$$100-\left(3\sqrt{7}\right)^{2}$$

Expand \left(3\sqrt{7}\right)^{2}.

$$100-3^{2}\left(\sqrt{7}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$100-9\left(\sqrt{7}\right)^{2}$$

The square of \sqrt{7} is 7.

$$100-9\times 7$$

Multiply 9 and 7 to get 63.

$$100-63$$

Subtract 63 from 100 to get 37.

$$37$$

Factor

$$37$$