Solve sqrt{98/856}*sqrt{9*7^2/45^2div789^2}

$$\sqrt{ \frac{ 98 }{ 856 } } \times \sqrt{ \frac{ 9 \times { 7 }^{ 2 } }{ { 45 }^{ 2 } \div { 789 }^{ 2 } } }$$

Evaluate

$$\frac{12887\sqrt{107}}{1070}\approx 124.583331343$$

Solution Steps

Reduce the fraction \frac{98}{856} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{49}{428}}\sqrt{\frac{9\times 7^{2}}{\frac{45^{2}}{789^{2}}}}$$

Rewrite the square root of the division \sqrt{\frac{49}{428}} as the division of square roots \frac{\sqrt{49}}{\sqrt{428}}.

$$\frac{\sqrt{49}}{\sqrt{428}}\sqrt{\frac{9\times 7^{2}}{\frac{45^{2}}{789^{2}}}}$$

Calculate the square root of 49 and get 7.

$$\frac{7}{\sqrt{428}}\sqrt{\frac{9\times 7^{2}}{\frac{45^{2}}{789^{2}}}}$$

Factor 428=2^{2}\times 107. Rewrite the square root of the product \sqrt{2^{2}\times 107} as the product of square roots \sqrt{2^{2}}\sqrt{107}. Take the square root of 2^{2}.

$$\frac{7}{2\sqrt{107}}\sqrt{\frac{9\times 7^{2}}{\frac{45^{2}}{789^{2}}}}$$

Rationalize the denominator of \frac{7}{2\sqrt{107}} by multiplying numerator and denominator by \sqrt{107}.

$$\frac{7\sqrt{107}}{2\left(\sqrt{107}\right)^{2}}\sqrt{\frac{9\times 7^{2}}{\frac{45^{2}}{789^{2}}}}$$

The square of \sqrt{107} is 107.

$$\frac{7\sqrt{107}}{2\times 107}\sqrt{\frac{9\times 7^{2}}{\frac{45^{2}}{789^{2}}}}$$

Multiply 2 and 107 to get 214.

$$\frac{7\sqrt{107}}{214}\sqrt{\frac{9\times 7^{2}}{\frac{45^{2}}{789^{2}}}}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{7\sqrt{107}}{214}\sqrt{\frac{9\times 49}{\frac{45^{2}}{789^{2}}}}$$

Multiply 9 and 49 to get 441.

$$\frac{7\sqrt{107}}{214}\sqrt{\frac{441}{\frac{45^{2}}{789^{2}}}}$$

Calculate 45 to the power of 2 and get 2025.

$$\frac{7\sqrt{107}}{214}\sqrt{\frac{441}{\frac{2025}{789^{2}}}}$$

Calculate 789 to the power of 2 and get 622521.

$$\frac{7\sqrt{107}}{214}\sqrt{\frac{441}{\frac{2025}{622521}}}$$

Reduce the fraction \frac{2025}{622521} to lowest terms by extracting and canceling out 9.

$$\frac{7\sqrt{107}}{214}\sqrt{\frac{441}{\frac{225}{69169}}}$$

Divide 441 by \frac{225}{69169} by multiplying 441 by the reciprocal of \frac{225}{69169}.

$$\frac{7\sqrt{107}}{214}\sqrt{441\times \frac{69169}{225}}$$

Express 441\times \frac{69169}{225} as a single fraction.

$$\frac{7\sqrt{107}}{214}\sqrt{\frac{441\times 69169}{225}}$$

Multiply 441 and 69169 to get 30503529.

$$\frac{7\sqrt{107}}{214}\sqrt{\frac{30503529}{225}}$$

Reduce the fraction \frac{30503529}{225} to lowest terms by extracting and canceling out 9.

$$\frac{7\sqrt{107}}{214}\sqrt{\frac{3389281}{25}}$$

Rewrite the square root of the division \frac{3389281}{25} as the division of square roots \frac{\sqrt{3389281}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$\frac{7\sqrt{107}}{214}\times \frac{1841}{5}$$

Multiply \frac{7\sqrt{107}}{214} times \frac{1841}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\sqrt{107}\times 1841}{214\times 5}$$

Multiply 7 and 1841 to get 12887.

$$\frac{12887\sqrt{107}}{214\times 5}$$

Multiply 214 and 5 to get 1070.

$$\frac{12887\sqrt{107}}{1070}$$