Solve [100+369/8-sqrt{66}div9-8/9]*6

$$[ 100 + \frac { 369 } { 8 } - \sqrt { 66 } \div \frac { 9 - 8 } { 9 } ] \times 6$$

Evaluate

$$\frac{3507}{4}-54\sqrt{66}\approx 438.05192615$$

Solution Steps

Convert 100 to fraction \frac{800}{8}.

$$6\left(\frac{800}{8}+\frac{369}{8}-\frac{\sqrt{66}}{\frac{9-8}{9}}\right)$$

Since \frac{800}{8} and \frac{369}{8} have the same denominator, add them by adding their numerators.

$$6\left(\frac{800+369}{8}-\frac{\sqrt{66}}{\frac{9-8}{9}}\right)$$

Add 800 and 369 to get 1169.

$$6\left(\frac{1169}{8}-\frac{\sqrt{66}}{\frac{9-8}{9}}\right)$$

Divide \sqrt{66} by \frac{9-8}{9} by multiplying \sqrt{66} by the reciprocal of \frac{9-8}{9}.

$$6\left(\frac{1169}{8}-\frac{\sqrt{66}\times 9}{9-8}\right)$$

Subtract 8 from 9 to get 1.

$$6\left(\frac{1169}{8}-\frac{\sqrt{66}\times 9}{1}\right)$$

Anything divided by one gives itself.

$$6\left(\frac{1169}{8}-\sqrt{66}\times 9\right)$$

Use the distributive property to multiply 6 by \frac{1169}{8}-\sqrt{66}\times 9.

$$6\times \frac{1169}{8}+6\left(-\sqrt{66}\times 9\right)$$

Express 6\times \frac{1169}{8} as a single fraction.

$$\frac{6\times 1169}{8}+6\left(-\sqrt{66}\times 9\right)$$

Multiply 6 and 1169 to get 7014.

$$\frac{7014}{8}+6\left(-\sqrt{66}\times 9\right)$$

Reduce the fraction \frac{7014}{8} to lowest terms by extracting and canceling out 2.

$$\frac{3507}{4}+6\left(-\sqrt{66}\times 9\right)$$

Multiply 6 and -1 to get -6.

$$\frac{3507}{4}-6\sqrt{66}\times 9$$

Multiply -6 and 9 to get -54.

$$\frac{3507}{4}-54\sqrt{66}$$

Factor

$$\frac{3 {(1169 - 72 \sqrt{66})}}{4} = 438.0519261496581$$