Solve sqrt{2^5*3^10*7^11}

$$\sqrt { 2 ^ { 5 } \cdot 3 ^ { 10 } \cdot 7 ^ { 11 } }$$

Evaluate

$$16336404\sqrt{14}\approx 61125226.699923359$$

Solution Steps

Calculate 2 to the power of 5 and get 32.

$$\sqrt{32\times 3^{10}\times 7^{11}}$$

Calculate 3 to the power of 10 and get 59049.

$$\sqrt{32\times 59049\times 7^{11}}$$

Multiply 32 and 59049 to get 1889568.

$$\sqrt{1889568\times 7^{11}}$$

Calculate 7 to the power of 11 and get 1977326743.

$$\sqrt{1889568\times 1977326743}$$

Multiply 1889568 and 1977326743 to get 3736293339117024.

$$\sqrt{3736293339117024}$$

Factor 3736293339117024=16336404^{2}\times 14. Rewrite the square root of the product \sqrt{16336404^{2}\times 14} as the product of square roots \sqrt{16336404^{2}}\sqrt{14}. Take the square root of 16336404^{2}.

$$16336404\sqrt{14}$$