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

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

Evaluate

$$7-2\sqrt{10}\approx 0.67544468$$

Solution Steps

Multiply \sqrt{5}-\sqrt{2} and \sqrt{5}-\sqrt{2} to get \left(\sqrt{5}-\sqrt{2}\right)^{2}.

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

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\sqrt{5}-\sqrt{2}\right)^{2}.

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

The square of \sqrt{5} is 5.

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

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

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

The square of \sqrt{2} is 2.

$$5-2\sqrt{10}+2$$

Add 5 and 2 to get 7.

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

Factor

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