Solve sqrt{10*7^2}*sqrt{10*2^6}

$$\sqrt { 10 \cdot 7 ^ { 2 } } \cdot \sqrt { 10 \cdot 2 ^ { 6 } }$$

Evaluate

$$560$$

Solution Steps

Calculate 7 to the power of 2 and get 49.

$$\sqrt{10\times 49}\sqrt{10\times 2^{6}}$$

Multiply 10 and 49 to get 490.

$$\sqrt{490}\sqrt{10\times 2^{6}}$$

Factor 490=7^{2}\times 10. Rewrite the square root of the product \sqrt{7^{2}\times 10} as the product of square roots \sqrt{7^{2}}\sqrt{10}. Take the square root of 7^{2}.

$$7\sqrt{10}\sqrt{10\times 2^{6}}$$

Calculate 2 to the power of 6 and get 64.

$$7\sqrt{10}\sqrt{10\times 64}$$

Multiply 10 and 64 to get 640.

$$7\sqrt{10}\sqrt{640}$$

Factor 640=8^{2}\times 10. Rewrite the square root of the product \sqrt{8^{2}\times 10} as the product of square roots \sqrt{8^{2}}\sqrt{10}. Take the square root of 8^{2}.

$$7\sqrt{10}\times 8\sqrt{10}$$

Multiply 7 and 8 to get 56.

$$56\sqrt{10}\sqrt{10}$$

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

$$56\times 10$$

Multiply 56 and 10 to get 560.

$$560$$

Factor

$$2^{4}\times 5\times 7$$