Solve 11-3*5+50:21^2:1-101divsqrt{9*2+7}=

$$11 - 3 \cdot 5 + 50 : 21 ^ { 2 } : 1 - 101 \div \sqrt { 9 \cdot 2 + 7 } =$$

Evaluate

$$-\frac{53111}{2205}\approx -24.086621315$$

Solution Steps

Multiply 3 and 5 to get 15.

$$11-15+\frac{\frac{50}{21^{2}}}{1}-\frac{101}{\sqrt{9\times 2+7}}$$

Subtract 15 from 11 to get -4.

$$-4+\frac{\frac{50}{21^{2}}}{1}-\frac{101}{\sqrt{9\times 2+7}}$$

Calculate 21 to the power of 2 and get 441.

$$-4+\frac{\frac{50}{441}}{1}-\frac{101}{\sqrt{9\times 2+7}}$$

Anything divided by one gives itself.

$$-4+\frac{50}{441}-\frac{101}{\sqrt{9\times 2+7}}$$

Convert -4 to fraction -\frac{1764}{441}.

$$-\frac{1764}{441}+\frac{50}{441}-\frac{101}{\sqrt{9\times 2+7}}$$

Since -\frac{1764}{441} and \frac{50}{441} have the same denominator, add them by adding their numerators.

$$\frac{-1764+50}{441}-\frac{101}{\sqrt{9\times 2+7}}$$

Add -1764 and 50 to get -1714.

$$-\frac{1714}{441}-\frac{101}{\sqrt{9\times 2+7}}$$

Multiply 9 and 2 to get 18.

$$-\frac{1714}{441}-\frac{101}{\sqrt{18+7}}$$

Add 18 and 7 to get 25.

$$-\frac{1714}{441}-\frac{101}{\sqrt{25}}$$

Calculate the square root of 25 and get 5.

$$-\frac{1714}{441}-\frac{101}{5}$$

Least common multiple of 441 and 5 is 2205. Convert -\frac{1714}{441} and \frac{101}{5} to fractions with denominator 2205.

$$-\frac{8570}{2205}-\frac{44541}{2205}$$

Since -\frac{8570}{2205} and \frac{44541}{2205} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-8570-44541}{2205}$$

Subtract 44541 from -8570 to get -53111.

$$-\frac{53111}{2205}$$

Factor

$$-\frac{53111}{2205} = -24\frac{191}{2205} = -24.086621315192744$$