Solve sqrt{7000}*5/8+sqrt{4000}*3/8

$$\sqrt { 7000 } \times \frac { 5 } { 8 } + \sqrt { 4000 } \times \frac { 3 } { 8 }$$

Evaluate

$$\frac{15\sqrt{10}}{2}+\frac{25\sqrt{70}}{4}\approx 76.00833411$$

Solution Steps

Factor 7000=10^{2}\times 70. Rewrite the square root of the product \sqrt{10^{2}\times 70} as the product of square roots \sqrt{10^{2}}\sqrt{70}. Take the square root of 10^{2}.

$$10\sqrt{70}\times \frac{5}{8}+\sqrt{4000}\times \frac{3}{8}$$

Express 10\times \frac{5}{8} as a single fraction.

$$\frac{10\times 5}{8}\sqrt{70}+\sqrt{4000}\times \frac{3}{8}$$

Multiply 10 and 5 to get 50.

$$\frac{50}{8}\sqrt{70}+\sqrt{4000}\times \frac{3}{8}$$

Reduce the fraction \frac{50}{8} to lowest terms by extracting and canceling out 2.

$$\frac{25}{4}\sqrt{70}+\sqrt{4000}\times \frac{3}{8}$$

Factor 4000=20^{2}\times 10. Rewrite the square root of the product \sqrt{20^{2}\times 10} as the product of square roots \sqrt{20^{2}}\sqrt{10}. Take the square root of 20^{2}.

$$\frac{25}{4}\sqrt{70}+20\sqrt{10}\times \frac{3}{8}$$

Express 20\times \frac{3}{8} as a single fraction.

$$\frac{25}{4}\sqrt{70}+\frac{20\times 3}{8}\sqrt{10}$$

Multiply 20 and 3 to get 60.

$$\frac{25}{4}\sqrt{70}+\frac{60}{8}\sqrt{10}$$

Reduce the fraction \frac{60}{8} to lowest terms by extracting and canceling out 4.

$$\frac{25}{4}\sqrt{70}+\frac{15}{2}\sqrt{10}$$

Factor

$$\frac{5 {(5 \sqrt{70} + 6 \sqrt{10})}}{4} = 76.00833410964258$$