Solve sqrt{10^6}-sqrt[3]{100^3}+sqrt{10^-4}-sqrt[3]{10^-6}

$$\sqrt { 10 ^ { 6 } } - \sqrt[ 3 ] { 100 ^ { 3 } } + \sqrt { 10 ^ { - 4 } } - \sqrt[ 3 ] { 10 ^ { - 6 } }$$

Evaluate

$$900$$

Solution Steps

Calculate 10 to the power of 6 and get 1000000.

$$\sqrt{1000000}-\sqrt[3]{100^{3}}+\sqrt{10^{-4}}-\sqrt[3]{10^{-6}}$$

Calculate the square root of 1000000 and get 1000.

$$1000-\sqrt[3]{100^{3}}+\sqrt{10^{-4}}-\sqrt[3]{10^{-6}}$$

Calculate 100 to the power of 3 and get 1000000.

$$1000-\sqrt[3]{1000000}+\sqrt{10^{-4}}-\sqrt[3]{10^{-6}}$$

Calculate \sqrt[3]{1000000} and get 100.

$$1000-100+\sqrt{10^{-4}}-\sqrt[3]{10^{-6}}$$

Subtract 100 from 1000 to get 900.

$$900+\sqrt{10^{-4}}-\sqrt[3]{10^{-6}}$$

Calculate 10 to the power of -4 and get \frac{1}{10000}.

$$900+\sqrt{\frac{1}{10000}}-\sqrt[3]{10^{-6}}$$

Rewrite the square root of the division \frac{1}{10000} as the division of square roots \frac{\sqrt{1}}{\sqrt{10000}}. Take the square root of both numerator and denominator.

$$900+\frac{1}{100}-\sqrt[3]{10^{-6}}$$

Add 900 and \frac{1}{100} to get \frac{90001}{100}.

$$\frac{90001}{100}-\sqrt[3]{10^{-6}}$$

Calculate 10 to the power of -6 and get \frac{1}{1000000}.

$$\frac{90001}{100}-\sqrt[3]{\frac{1}{1000000}}$$

Calculate \sqrt[3]{\frac{1}{1000000}} and get \frac{1}{100}.

$$\frac{90001}{100}-\frac{1}{100}$$

Subtract \frac{1}{100} from \frac{90001}{100} to get 900.

$$900$$

Factor

$$2^{2}\times 3^{2}\times 5^{2}$$