Solve sqrt{2^5*3^2*7^3}=

$$\sqrt { 2 ^ { 5 } \times 3 ^ { 2 } \times 7 ^ { 3 } } =$$

Evaluate

$$84\sqrt{14}\approx 314.299220489$$

Solution Steps

Calculate 2 to the power of 5 and get 32.

$$\sqrt{32\times 3^{2}\times 7^{3}}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{32\times 9\times 7^{3}}$$

Multiply 32 and 9 to get 288.

$$\sqrt{288\times 7^{3}}$$

Calculate 7 to the power of 3 and get 343.

$$\sqrt{288\times 343}$$

Multiply 288 and 343 to get 98784.

$$\sqrt{98784}$$

Factor 98784=84^{2}\times 14. Rewrite the square root of the product \sqrt{84^{2}\times 14} as the product of square roots \sqrt{84^{2}}\sqrt{14}. Take the square root of 84^{2}.

$$84\sqrt{14}$$