Solve sqrt{669/frac{39616{669}}}

$$\sqrt{ \frac{ 669 }{ \frac{ 39616 }{ 669 } } }$$

Evaluate

$$\frac{669\sqrt{619}}{4952}\approx 3.361172536$$

Solution Steps

Divide 669 by \frac{39616}{669} by multiplying 669 by the reciprocal of \frac{39616}{669}.

$$\sqrt{669\times \frac{669}{39616}}$$

Express 669\times \frac{669}{39616} as a single fraction.

$$\sqrt{\frac{669\times 669}{39616}}$$

Multiply 669 and 669 to get 447561.

$$\sqrt{\frac{447561}{39616}}$$

Rewrite the square root of the division \sqrt{\frac{447561}{39616}} as the division of square roots \frac{\sqrt{447561}}{\sqrt{39616}}.

$$\frac{\sqrt{447561}}{\sqrt{39616}}$$

Calculate the square root of 447561 and get 669.

$$\frac{669}{\sqrt{39616}}$$

Factor 39616=8^{2}\times 619. Rewrite the square root of the product \sqrt{8^{2}\times 619} as the product of square roots \sqrt{8^{2}}\sqrt{619}. Take the square root of 8^{2}.

$$\frac{669}{8\sqrt{619}}$$

Rationalize the denominator of \frac{669}{8\sqrt{619}} by multiplying numerator and denominator by \sqrt{619}.

$$\frac{669\sqrt{619}}{8\left(\sqrt{619}\right)^{2}}$$

The square of \sqrt{619} is 619.

$$\frac{669\sqrt{619}}{8\times 619}$$

Multiply 8 and 619 to get 4952.

$$\frac{669\sqrt{619}}{4952}$$