Solve sqrt{4sqrt{5sqrt{6sqrt{7sqrt{2sqrt{0sqrt{9sqrt{01sqrt{8}}}}}}}}}

$$\sqrt{ 4 \sqrt{ 5 \sqrt{ 6 \sqrt{ 7 \sqrt{ 2 \sqrt{ 0 \sqrt{ 9 \sqrt{ 01 \sqrt{ 8 } } } } } } } } }$$

Evaluate

$$0$$

Solution Steps

Multiply 0 and 1 to get 0.

$$\sqrt{4\sqrt{5\sqrt{6\sqrt{7\sqrt{2\sqrt{0\sqrt{9\sqrt{0\sqrt{8}}}}}}}}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\sqrt{4\sqrt{5\sqrt{6\sqrt{7\sqrt{2\sqrt{0\sqrt{9\sqrt{0\times 2\sqrt{2}}}}}}}}}$$

Multiply 0 and 2 to get 0.

$$\sqrt{4\sqrt{5\sqrt{6\sqrt{7\sqrt{2\sqrt{0\sqrt{9\sqrt{0\sqrt{2}}}}}}}}}$$

Anything times zero gives zero.

$$\sqrt{4\sqrt{5\sqrt{6\sqrt{7\sqrt{2\sqrt{0\sqrt{9\sqrt{0}}}}}}}}$$

Calculate the square root of 0 and get 0.

$$\sqrt{4\sqrt{5\sqrt{6\sqrt{7\sqrt{2\sqrt{0\sqrt{9\times 0}}}}}}}$$

Multiply 9 and 0 to get 0.

$$\sqrt{4\sqrt{5\sqrt{6\sqrt{7\sqrt{2\sqrt{0\sqrt{0}}}}}}}$$

Calculate the square root of 0 and get 0.

$$\sqrt{4\sqrt{5\sqrt{6\sqrt{7\sqrt{2\sqrt{0\times 0}}}}}}$$

Multiply 0 and 0 to get 0.

$$\sqrt{4\sqrt{5\sqrt{6\sqrt{7\sqrt{2\sqrt{0}}}}}}$$

Calculate the square root of 0 and get 0.

$$\sqrt{4\sqrt{5\sqrt{6\sqrt{7\sqrt{2\times 0}}}}}$$

Multiply 2 and 0 to get 0.

$$\sqrt{4\sqrt{5\sqrt{6\sqrt{7\sqrt{0}}}}}$$

Calculate the square root of 0 and get 0.

$$\sqrt{4\sqrt{5\sqrt{6\sqrt{7\times 0}}}}$$

Multiply 7 and 0 to get 0.

$$\sqrt{4\sqrt{5\sqrt{6\sqrt{0}}}}$$

Calculate the square root of 0 and get 0.

$$\sqrt{4\sqrt{5\sqrt{6\times 0}}}$$

Multiply 6 and 0 to get 0.

$$\sqrt{4\sqrt{5\sqrt{0}}}$$

Calculate the square root of 0 and get 0.

$$\sqrt{4\sqrt{5\times 0}}$$

Multiply 5 and 0 to get 0.

$$\sqrt{4\sqrt{0}}$$

Calculate the square root of 0 and get 0.

$$\sqrt{4\times 0}$$

Multiply 4 and 0 to get 0.

$$\sqrt{0}$$

Calculate the square root of 0 and get 0.

$$0$$

Factor

$$0$$