Solve 15+2[3(6+2)^1/3-2(4+1)]+[8(15-7)]^1/3

$$15 + 2 [ 3 ( 6 + 2 ) ^ { 1 / 3 } - 2 ( 4 + 1 ) ] + [ 8 ( 15 - 7 ) ] ^ { 1 / 3 }$$

Evaluate

$$11$$

Solution Steps

Add 6 and 2 to get 8.

$$15+2\left(3\times 8^{\frac{1}{3}}-2\left(4+1\right)\right)+\left(8\left(15-7\right)\right)^{\frac{1}{3}}$$

Calculate 8 to the power of \frac{1}{3} and get 2.

$$15+2\left(3\times 2-2\left(4+1\right)\right)+\left(8\left(15-7\right)\right)^{\frac{1}{3}}$$

Multiply 3 and 2 to get 6.

$$15+2\left(6-2\left(4+1\right)\right)+\left(8\left(15-7\right)\right)^{\frac{1}{3}}$$

Add 4 and 1 to get 5.

$$15+2\left(6-2\times 5\right)+\left(8\left(15-7\right)\right)^{\frac{1}{3}}$$

Multiply 2 and 5 to get 10.

$$15+2\left(6-10\right)+\left(8\left(15-7\right)\right)^{\frac{1}{3}}$$

Subtract 10 from 6 to get -4.

$$15+2\left(-4\right)+\left(8\left(15-7\right)\right)^{\frac{1}{3}}$$

Multiply 2 and -4 to get -8.

$$15-8+\left(8\left(15-7\right)\right)^{\frac{1}{3}}$$

Subtract 8 from 15 to get 7.

$$7+\left(8\left(15-7\right)\right)^{\frac{1}{3}}$$

Subtract 7 from 15 to get 8.

$$7+\left(8\times 8\right)^{\frac{1}{3}}$$

Multiply 8 and 8 to get 64.

$$7+64^{\frac{1}{3}}$$

Calculate 64 to the power of \frac{1}{3} and get 4.

$$7+4$$

Add 7 and 4 to get 11.

$$11$$

Factor

$$11$$