Solve frac{sqrt{12}*6^3}{24+8}-56+8^20-36

$$\frac { \sqrt { 12 } \times 6 ^ { 3 } } { 24 + 8 } - 56 + 8 ^ { 20 } - 36$$

Evaluate

$$\frac{27\sqrt{3}}{2}+1152921504606846884\approx 1.152921505 \cdot 10^{18}$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{2\sqrt{3}\times 6^{3}}{24+8}-56+8^{20}-36$$

Calculate 6 to the power of 3 and get 216.

$$\frac{2\sqrt{3}\times 216}{24+8}-56+8^{20}-36$$

Multiply 2 and 216 to get 432.

$$\frac{432\sqrt{3}}{24+8}-56+8^{20}-36$$

Add 24 and 8 to get 32.

$$\frac{432\sqrt{3}}{32}-56+8^{20}-36$$

Divide 432\sqrt{3} by 32 to get \frac{27}{2}\sqrt{3}.

$$\frac{27}{2}\sqrt{3}-56+8^{20}-36$$

Calculate 8 to the power of 20 and get 1152921504606846976.

$$\frac{27}{2}\sqrt{3}-56+1152921504606846976-36$$

Add -56 and 1152921504606846976 to get 1152921504606846920.

$$\frac{27}{2}\sqrt{3}+1152921504606846920-36$$

Subtract 36 from 1152921504606846920 to get 1152921504606846884.

$$\frac{27}{2}\sqrt{3}+1152921504606846884$$