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

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

Evaluate

$$3$$

Solution Steps

To find the opposite of \sqrt{2}-\sqrt{5}, find the opposite of each term.

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

The opposite of -\sqrt{5} is \sqrt{5}.

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

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

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

The square of \sqrt{2} is 2.

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

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

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

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

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

Combine -\sqrt{10} and \sqrt{10} to get 0.

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

The square of \sqrt{5} is 5.

$$-2+5$$

Add -2 and 5 to get 3.

$$3$$

Factor

$$3$$