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

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

Evaluate

$$14$$

Solution Steps

Calculate 2 to the power of 3 and get 8.

$$\frac{\sqrt{8\times 7^{5}}}{\sqrt{2\times 7^{3}}}$$

Calculate 7 to the power of 5 and get 16807.

$$\frac{\sqrt{8\times 16807}}{\sqrt{2\times 7^{3}}}$$

Multiply 8 and 16807 to get 134456.

$$\frac{\sqrt{134456}}{\sqrt{2\times 7^{3}}}$$

Factor 134456=98^{2}\times 14. Rewrite the square root of the product \sqrt{98^{2}\times 14} as the product of square roots \sqrt{98^{2}}\sqrt{14}. Take the square root of 98^{2}.

$$\frac{98\sqrt{14}}{\sqrt{2\times 7^{3}}}$$

Calculate 7 to the power of 3 and get 343.

$$\frac{98\sqrt{14}}{\sqrt{2\times 343}}$$

Multiply 2 and 343 to get 686.

$$\frac{98\sqrt{14}}{\sqrt{686}}$$

Factor 686=7^{2}\times 14. Rewrite the square root of the product \sqrt{7^{2}\times 14} as the product of square roots \sqrt{7^{2}}\sqrt{14}. Take the square root of 7^{2}.

$$\frac{98\sqrt{14}}{7\sqrt{14}}$$

Cancel out 7\sqrt{14} in both numerator and denominator.

$$14$$

Factor

$$2\times 7$$