Solve sqrt{9+sqrt[4]{81}+sqrt[3]{1}-sqrt[4]{3^8}}

$$\sqrt { 9 + \sqrt[ 4 ] { 81 } + \sqrt[ 3 ] { 1 } - \sqrt[ 4 ] { 3 ^ { 8 } } }$$

Evaluate

$$2$$

Solution Steps

Calculate \sqrt[4]{81} and get 3.

$$\sqrt{9+3+\sqrt[3]{1}-\sqrt[4]{3^{8}}}$$

Add 9 and 3 to get 12.

$$\sqrt{12+\sqrt[3]{1}-\sqrt[4]{3^{8}}}$$

Calculate \sqrt[3]{1} and get 1.

$$\sqrt{12+1-\sqrt[4]{3^{8}}}$$

Add 12 and 1 to get 13.

$$\sqrt{13-\sqrt[4]{3^{8}}}$$

Calculate 3 to the power of 8 and get 6561.

$$\sqrt{13-\sqrt[4]{6561}}$$

Calculate \sqrt[4]{6561} and get 9.

$$\sqrt{13-9}$$

Subtract 9 from 13 to get 4.

$$\sqrt{4}$$

Calculate the square root of 4 and get 2.

$$2$$

Factor

$$2$$