Solve sqrt{5}*2sqrt{8}-sqrt{5}-2sqrt{6}

$$\sqrt { 5 } \cdot 2 \sqrt { 8 } - \sqrt { 5 } - 2 \sqrt { 6 }$$

Evaluate

$$4\sqrt{10}-\sqrt{5}-2\sqrt{6}\approx 5.514063178$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$2\sqrt{5}\times 2\sqrt{2}-\sqrt{5}-2\sqrt{6}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{5}\sqrt{2}-\sqrt{5}-2\sqrt{6}$$

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

$$4\sqrt{10}-\sqrt{5}-2\sqrt{6}$$