Solve sqrt{5}(4sqrt{10}+7sqrt{15)}

$$\sqrt{ 5 } (4 \sqrt{ 10 } +7 \sqrt{ 15) }$$

Evaluate

$$20\sqrt{2}+35\sqrt{3}\approx 88.906049512$$

Solution Steps

Use the distributive property to multiply \sqrt{5} by 4\sqrt{10}+7\sqrt{15}.

$$4\sqrt{5}\sqrt{10}+7\sqrt{5}\sqrt{15}$$

Factor 10=5\times 2. Rewrite the square root of the product \sqrt{5\times 2} as the product of square roots \sqrt{5}\sqrt{2}.

$$4\sqrt{5}\sqrt{5}\sqrt{2}+7\sqrt{5}\sqrt{15}$$

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

$$4\times 5\sqrt{2}+7\sqrt{5}\sqrt{15}$$

Multiply 4 and 5 to get 20.

$$20\sqrt{2}+7\sqrt{5}\sqrt{15}$$

Factor 15=5\times 3. Rewrite the square root of the product \sqrt{5\times 3} as the product of square roots \sqrt{5}\sqrt{3}.

$$20\sqrt{2}+7\sqrt{5}\sqrt{5}\sqrt{3}$$

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

$$20\sqrt{2}+7\times 5\sqrt{3}$$

Multiply 7 and 5 to get 35.

$$20\sqrt{2}+35\sqrt{3}$$