Solve 25/3sqrt{2*sqrt{42}}

$$\frac { 25 } { 3 \sqrt { 2 } \cdot \sqrt { 42 } }$$

Evaluate

$$\frac{25\sqrt{21}}{126}\approx 0.909241209$$

Solution Steps

Factor 42=2\times 21. Rewrite the square root of the product \sqrt{2\times 21} as the product of square roots \sqrt{2}\sqrt{21}.

$$\frac{25}{3\sqrt{2}\sqrt{2}\sqrt{21}}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{25}{3\times 2\sqrt{21}}$$

Multiply 3 and 2 to get 6.

$$\frac{25}{6\sqrt{21}}$$

Rationalize the denominator of \frac{25}{6\sqrt{21}} by multiplying numerator and denominator by \sqrt{21}.

$$\frac{25\sqrt{21}}{6\left(\sqrt{21}\right)^{2}}$$

The square of \sqrt{21} is 21.

$$\frac{25\sqrt{21}}{6\times 21}$$

Multiply 6 and 21 to get 126.

$$\frac{25\sqrt{21}}{126}$$