Solve sqrt[3]{1+sqrt{36}+sqrt[3]{-8}+sqrt{left((-3)right)^2}}

$$\sqrt[3]{ 1+ \sqrt{ 36 } + \sqrt[3]{ -8 } + \sqrt{ { \left((-3) \right) }^{ 2 } } }$$

Evaluate

$$2$$

Solution Steps

Calculate the square root of 36 and get 6.

$$\sqrt[3]{1+6+\sqrt[3]{-8}+\sqrt{\left(-3\right)^{2}}}$$

Add 1 and 6 to get 7.

$$\sqrt[3]{7+\sqrt[3]{-8}+\sqrt{\left(-3\right)^{2}}}$$

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

$$\sqrt[3]{7-2+\sqrt{\left(-3\right)^{2}}}$$

Subtract 2 from 7 to get 5.

$$\sqrt[3]{5+\sqrt{\left(-3\right)^{2}}}$$

Calculate -3 to the power of 2 and get 9.

$$\sqrt[3]{5+\sqrt{9}}$$

Calculate the square root of 9 and get 3.

$$\sqrt[3]{5+3}$$

Add 5 and 3 to get 8.

$$\sqrt[3]{8}$$

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

$$2$$

Factor

$$2$$