Solve sqrt{124}-8*3div(-12)+40div(-8)-(15)x^3sqrt[3]{-8}

$$\sqrt { 124 } - 8 \times 3 \div ( - 12 ) + 40 \div ( - 8 ) - ( 15 ) x ^ { 3 } \sqrt[ 3 ] { - 8 }$$

Evaluate

$$30x^{3}+2\sqrt{31}-3$$

Solution Steps

Factor 124=2^{2}\times 31. Rewrite the square root of the product \sqrt{2^{2}\times 31} as the product of square roots \sqrt{2^{2}}\sqrt{31}. Take the square root of 2^{2}.

$$2\sqrt{31}-\frac{8\times 3}{-12}+\frac{40}{-8}-15x^{3}\sqrt[3]{-8}$$

Multiply 8 and 3 to get 24.

$$2\sqrt{31}-\frac{24}{-12}+\frac{40}{-8}-15x^{3}\sqrt[3]{-8}$$

Divide 24 by -12 to get -2.

$$2\sqrt{31}-\left(-2\right)+\frac{40}{-8}-15x^{3}\sqrt[3]{-8}$$

The opposite of -2 is 2.

$$2\sqrt{31}+2+\frac{40}{-8}-15x^{3}\sqrt[3]{-8}$$

Divide 40 by -8 to get -5.

$$2\sqrt{31}+2-5-15x^{3}\sqrt[3]{-8}$$

Subtract 5 from 2 to get -3.

$$2\sqrt{31}-3-15x^{3}\sqrt[3]{-8}$$

Calculate \sqrt[3]{-8} and get -2.

$$2\sqrt{31}-3-15x^{3}\left(-2\right)$$

Multiply 15 and -2 to get -30.

$$2\sqrt{31}-3-\left(-30x^{3}\right)$$

The opposite of -30x^{3} is 30x^{3}.

$$2\sqrt{31}-3+30x^{3}$$

Differentiate w.r.t. x

$$90x^{2}$$