Solve (sqrt{5}-sqrt{2})(sqrt{2}-sqrt{7})

$$( \sqrt { 5 } - \sqrt { 2 } ) ( \sqrt { 2 } - \sqrt { 7 } )$$

Evaluate

$$\sqrt{10}+\sqrt{14}-\sqrt{35}-2\approx -1.012144736$$

Solution Steps

Apply the distributive property by multiplying each term of \sqrt{5}-\sqrt{2} by each term of \sqrt{2}-\sqrt{7}.

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

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

$$\sqrt{10}-\sqrt{5}\sqrt{7}-\left(\sqrt{2}\right)^{2}+\sqrt{2}\sqrt{7}$$

To multiply \sqrt{5} and \sqrt{7}, multiply the numbers under the square root.

$$\sqrt{10}-\sqrt{35}-\left(\sqrt{2}\right)^{2}+\sqrt{2}\sqrt{7}$$

The square of \sqrt{2} is 2.

$$\sqrt{10}-\sqrt{35}-2+\sqrt{2}\sqrt{7}$$

To multiply \sqrt{2} and \sqrt{7}, multiply the numbers under the square root.

$$\sqrt{10}-\sqrt{35}-2+\sqrt{14}$$