Solve (frac{sqrt{52}9-4^3-3}{4^2})-[52(2)/23]

$$( \frac { \sqrt { 52 } 9 - 4 ^ { 3 } - 3 } { 4 ^ { 2 } } ) - [ \frac { 52 ( 2 ) } { 23 } ]$$

Evaluate

$$\frac{9\sqrt{13}}{8}-\frac{3205}{368}\approx -4.652993946$$

Short Solution Steps

Factor 52=2^{2}\times 13. Rewrite the square root of the product \sqrt{2^{2}\times 13} as the product of square roots \sqrt{2^{2}}\sqrt{13}. Take the square root of 2^{2}.

$$\frac{9\times 2\sqrt{13}-4^{3}-3}{4^{2}}-\frac{52\times 2}{23}$$

Multiply 9 and 2 to get 18.

$$\frac{18\sqrt{13}-4^{3}-3}{4^{2}}-\frac{52\times 2}{23}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{18\sqrt{13}-64-3}{4^{2}}-\frac{52\times 2}{23}$$

Subtract 3 from -64 to get -67.

$$\frac{18\sqrt{13}-67}{4^{2}}-\frac{52\times 2}{23}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{18\sqrt{13}-67}{16}-\frac{52\times 2}{23}$$

Multiply 52 and 2 to get 104.

$$\frac{18\sqrt{13}-67}{16}-\frac{104}{23}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 16 and 23 is 368. Multiply \frac{18\sqrt{13}-67}{16} times \frac{23}{23}. Multiply \frac{104}{23} times \frac{16}{16}.

$$\frac{23\left(18\sqrt{13}-67\right)}{368}-\frac{104\times 16}{368}$$

Since \frac{23\left(18\sqrt{13}-67\right)}{368} and \frac{104\times 16}{368} have the same denominator, subtract them by subtracting their numerators.

$$\frac{23\left(18\sqrt{13}-67\right)-104\times 16}{368}$$

Do the multiplications in 23\left(18\sqrt{13}-67\right)-104\times 16.

$$\frac{414\sqrt{13}-1541-1664}{368}$$

Do the calculations in 414\sqrt{13}-1541-1664.

$$\frac{414\sqrt{13}-3205}{368}$$

Factor

$$\frac{414 \sqrt{13} - 3205}{368} = -4.652993945537795$$