Solve sqrt{7000000}*5/8+sqrt{4000000}*3/8

$$\sqrt { 7000000 } \times \frac { 5 } { 8 } + \sqrt { 4000000 } \times \frac { 3 } { 8 }$$

Evaluate

$$625\sqrt{7}+750\approx 2403.594569415$$

Solution Steps

Factor 7000000=1000^{2}\times 7. Rewrite the square root of the product \sqrt{1000^{2}\times 7} as the product of square roots \sqrt{1000^{2}}\sqrt{7}. Take the square root of 1000^{2}.

$$1000\sqrt{7}\times \frac{5}{8}+\sqrt{4000000}\times \frac{3}{8}$$

Express 1000\times \frac{5}{8} as a single fraction.

$$\frac{1000\times 5}{8}\sqrt{7}+\sqrt{4000000}\times \frac{3}{8}$$

Multiply 1000 and 5 to get 5000.

$$\frac{5000}{8}\sqrt{7}+\sqrt{4000000}\times \frac{3}{8}$$

Divide 5000 by 8 to get 625.

$$625\sqrt{7}+\sqrt{4000000}\times \frac{3}{8}$$

Calculate the square root of 4000000 and get 2000.

$$625\sqrt{7}+2000\times \frac{3}{8}$$

Express 2000\times \frac{3}{8} as a single fraction.

$$625\sqrt{7}+\frac{2000\times 3}{8}$$

Multiply 2000 and 3 to get 6000.

$$625\sqrt{7}+\frac{6000}{8}$$

Divide 6000 by 8 to get 750.

$$625\sqrt{7}+750$$

Factor

$$125 {(5 \sqrt{7} + 6)} = 2403.594569415$$