Solve sqrt{30}div(sqrt{3}-sqrt{2})=

$$\sqrt { 30 } \div ( \sqrt { 3 } - \sqrt { 2 } ) =$$

Evaluate

$$2\sqrt{15}+3\sqrt{10}\approx 17.232799673$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{30}}{\sqrt{3}-\sqrt{2}} by multiplying numerator and denominator by \sqrt{3}+\sqrt{2}.

$$\frac{\sqrt{30}\left(\sqrt{3}+\sqrt{2}\right)}{\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)}$$

Consider \left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\sqrt{30}\left(\sqrt{3}+\sqrt{2}\right)}{\left(\sqrt{3}\right)^{2}-\left(\sqrt{2}\right)^{2}}$$

Square \sqrt{3}. Square \sqrt{2}.

$$\frac{\sqrt{30}\left(\sqrt{3}+\sqrt{2}\right)}{3-2}$$

Subtract 2 from 3 to get 1.

$$\frac{\sqrt{30}\left(\sqrt{3}+\sqrt{2}\right)}{1}$$

Anything divided by one gives itself.

$$\sqrt{30}\left(\sqrt{3}+\sqrt{2}\right)$$

Use the distributive property to multiply \sqrt{30} by \sqrt{3}+\sqrt{2}.

$$\sqrt{30}\sqrt{3}+\sqrt{30}\sqrt{2}$$

Factor 30=3\times 10. Rewrite the square root of the product \sqrt{3\times 10} as the product of square roots \sqrt{3}\sqrt{10}.

$$\sqrt{3}\sqrt{10}\sqrt{3}+\sqrt{30}\sqrt{2}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$3\sqrt{10}+\sqrt{30}\sqrt{2}$$

Factor 30=2\times 15. Rewrite the square root of the product \sqrt{2\times 15} as the product of square roots \sqrt{2}\sqrt{15}.

$$3\sqrt{10}+\sqrt{2}\sqrt{15}\sqrt{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$3\sqrt{10}+2\sqrt{15}$$