Solve sqrt{2^4*7^3}*sqrt{8*49^2}

$$\sqrt { 2 ^ { 4 } \cdot 7 ^ { 3 } } \cdot \sqrt { 8 \cdot 49 ^ { 2 } }$$

Evaluate

$$2744\sqrt{14}\approx 10267.107869308$$

Solution Steps

Calculate 2 to the power of 4 and get 16.

$$\sqrt{16\times 7^{3}}\sqrt{8\times 49^{2}}$$

Calculate 7 to the power of 3 and get 343.

$$\sqrt{16\times 343}\sqrt{8\times 49^{2}}$$

Multiply 16 and 343 to get 5488.

$$\sqrt{5488}\sqrt{8\times 49^{2}}$$

Factor 5488=28^{2}\times 7. Rewrite the square root of the product \sqrt{28^{2}\times 7} as the product of square roots \sqrt{28^{2}}\sqrt{7}. Take the square root of 28^{2}.

$$28\sqrt{7}\sqrt{8\times 49^{2}}$$

Calculate 49 to the power of 2 and get 2401.

$$28\sqrt{7}\sqrt{8\times 2401}$$

Multiply 8 and 2401 to get 19208.

$$28\sqrt{7}\sqrt{19208}$$

Factor 19208=98^{2}\times 2. Rewrite the square root of the product \sqrt{98^{2}\times 2} as the product of square roots \sqrt{98^{2}}\sqrt{2}. Take the square root of 98^{2}.

$$28\sqrt{7}\times 98\sqrt{2}$$

Multiply 28 and 98 to get 2744.

$$2744\sqrt{7}\sqrt{2}$$

To multiply \sqrt{7} and \sqrt{2}, multiply the numbers under the square root.

$$2744\sqrt{14}$$