Solve (sqrt{5}+sqrt{6})(sqrt{10}sqrt{12})

$$( \sqrt{ 5 } + \sqrt{ 6 } )( \sqrt{ 10 } \sqrt{ 12 } )$$

Evaluate

$$10\sqrt{6}+12\sqrt{5}\approx 51.327713158$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\left(\sqrt{5}+\sqrt{6}\right)\sqrt{10}\times 2\sqrt{3}$$

To multiply \sqrt{10} and \sqrt{3}, multiply the numbers under the square root.

$$\left(\sqrt{5}+\sqrt{6}\right)\sqrt{30}\times 2$$

Use the distributive property to multiply \sqrt{5}+\sqrt{6} by \sqrt{30}.

$$\left(\sqrt{5}\sqrt{30}+\sqrt{6}\sqrt{30}\right)\times 2$$

Factor 30=5\times 6. Rewrite the square root of the product \sqrt{5\times 6} as the product of square roots \sqrt{5}\sqrt{6}.

$$\left(\sqrt{5}\sqrt{5}\sqrt{6}+\sqrt{6}\sqrt{30}\right)\times 2$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\left(5\sqrt{6}+\sqrt{6}\sqrt{30}\right)\times 2$$

Factor 30=6\times 5. Rewrite the square root of the product \sqrt{6\times 5} as the product of square roots \sqrt{6}\sqrt{5}.

$$\left(5\sqrt{6}+\sqrt{6}\sqrt{6}\sqrt{5}\right)\times 2$$

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$\left(5\sqrt{6}+6\sqrt{5}\right)\times 2$$

Use the distributive property to multiply 5\sqrt{6}+6\sqrt{5} by 2.

$$10\sqrt{6}+12\sqrt{5}$$