Solve sqrt{left(2*5right)^7}1000sqrt{10}

$$\sqrt{ { \left(2 \cdot 5 \right) }^{ 7 } } 1000 \sqrt{ 10 }$$

Evaluate

$$10000000$$

Solution Steps

Multiply 2 and 5 to get 10.

$$1000\sqrt{10^{7}}\sqrt{10}$$

Calculate 10 to the power of 7 and get 10000000.

$$1000\sqrt{10000000}\sqrt{10}$$

Factor 10000000=1000^{2}\times 10. Rewrite the square root of the product \sqrt{1000^{2}\times 10} as the product of square roots \sqrt{1000^{2}}\sqrt{10}. Take the square root of 1000^{2}.

$$1000\times 1000\sqrt{10}\sqrt{10}$$

Multiply 1000 and 1000 to get 1000000.

$$1000000\sqrt{10}\sqrt{10}$$

Multiply \sqrt{10} and \sqrt{10} to get 10.

$$1000000\times 10$$

Multiply 1000000 and 10 to get 10000000.

$$10000000$$

Factor

$$2^{7}\times 5^{7}$$