Solve sqrt{42*105/169}

$$\sqrt{ \frac{ 42 \times 105 }{ 169 } }$$

Evaluate

$$\frac{21\sqrt{10}}{13}\approx 5.108294682$$

Solution Steps

Multiply 42 and 105 to get 4410.

$$\sqrt{\frac{4410}{169}}$$

Rewrite the square root of the division \sqrt{\frac{4410}{169}} as the division of square roots \frac{\sqrt{4410}}{\sqrt{169}}.

$$\frac{\sqrt{4410}}{\sqrt{169}}$$

Factor 4410=21^{2}\times 10. Rewrite the square root of the product \sqrt{21^{2}\times 10} as the product of square roots \sqrt{21^{2}}\sqrt{10}. Take the square root of 21^{2}.

$$\frac{21\sqrt{10}}{\sqrt{169}}$$

Calculate the square root of 169 and get 13.

$$\frac{21\sqrt{10}}{13}$$