Solve {l}{3200+300}{-2*40sqrt{2}}{*10sqrt{3}*frac{5sqrt{26}}{26}}

$$\left. \begin{array} { l } { 3200 + 300 } \\ { - 2 \times 40 \sqrt { 2 } } \\ { \times 10 \sqrt { 3 } \times \frac { 5 \sqrt { 26 } } { 26 } } \end{array} \right.$$

Evaluate

$$-\frac{4000\sqrt{39}}{13}+3500\approx 1578.462154339$$

Solution Steps

Add 3200 and 300 to get 3500.

$$3500-2\times 10\times 40\sqrt{2}\sqrt{3}\times \frac{5\sqrt{26}}{26}$$

Multiply 2 and 10 to get 20.

$$3500-20\times 40\sqrt{2}\sqrt{3}\times \frac{5\sqrt{26}}{26}$$

Multiply 20 and 40 to get 800.

$$3500-800\sqrt{2}\sqrt{3}\times \frac{5\sqrt{26}}{26}$$

Express 800\times \frac{5\sqrt{26}}{26} as a single fraction.

$$3500-\frac{800\times 5\sqrt{26}}{26}\sqrt{2}\sqrt{3}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$3500-\frac{800\times 5\sqrt{26}}{26}\sqrt{6}$$

Multiply 800 and 5 to get 4000.

$$3500-\frac{4000\sqrt{26}}{26}\sqrt{6}$$

Divide 4000\sqrt{26} by 26 to get \frac{2000}{13}\sqrt{26}.

$$3500-\frac{2000}{13}\sqrt{26}\sqrt{6}$$

To multiply \sqrt{26} and \sqrt{6}, multiply the numbers under the square root.

$$3500-\frac{2000}{13}\sqrt{156}$$

Factor 156=2^{2}\times 39. Rewrite the square root of the product \sqrt{2^{2}\times 39} as the product of square roots \sqrt{2^{2}}\sqrt{39}. Take the square root of 2^{2}.

$$3500-\frac{2000}{13}\times 2\sqrt{39}$$

Express -\frac{2000}{13}\times 2 as a single fraction.

$$3500+\frac{-2000\times 2}{13}\sqrt{39}$$

Multiply -2000 and 2 to get -4000.

$$3500+\frac{-4000}{13}\sqrt{39}$$

Fraction \frac{-4000}{13} can be rewritten as -\frac{4000}{13} by extracting the negative sign.

$$3500-\frac{4000}{13}\sqrt{39}$$

Factor

$$\frac{500 {(91 - 8 \sqrt{39})}}{13} = 1578.4621543389544$$