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

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

Evaluate

$$\sqrt{10}+8\approx 11.16227766$$

Solution Steps

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

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

The square of \sqrt{5} is 5.

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

Multiply 2 and 5 to get 10.

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

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

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

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

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

Combine -\sqrt{10} and 2\sqrt{10} to get \sqrt{10}.

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

The square of \sqrt{2} is 2.

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

Subtract 2 from 10 to get 8.

$$8+\sqrt{10}$$

Factor

$$\sqrt{10} + 8 = 11.16227766$$