Solve (12.5sqrt{10})(3sqrt{5}+3)

$$( 12.5 \sqrt { 10 } ) ( 3 \sqrt { 5 } + 3 )$$

Evaluate

$$\frac{75\sqrt{10}+375\sqrt{2}}{2}\approx 383.750455201$$

Solution Steps

Use the distributive property to multiply 12.5\sqrt{10} by 3\sqrt{5}+3.

$$37.5\sqrt{10}\sqrt{5}+37.5\sqrt{10}$$

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}.

$$37.5\sqrt{5}\sqrt{2}\sqrt{5}+37.5\sqrt{10}$$

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

$$37.5\times 5\sqrt{2}+37.5\sqrt{10}$$

Multiply 37.5 and 5 to get 187.5.

$$187.5\sqrt{2}+37.5\sqrt{10}$$

Factor

$$\frac{75 \sqrt{10} + 375 \sqrt{2}}{2} = 383.7504552012696$$