Solve 1/25quadsqrt{25/9*49}

$$\frac { 1 } { 25 } \quad \sqrt { \frac { 25 } { 9 \times 49 } }$$

Evaluate

$$\frac{1}{105}\approx 0.00952381$$

Solution Steps

Multiply 9 and 49 to get 441.

$$\frac{1}{25}\sqrt{\frac{25}{441}}$$

Rewrite the square root of the division \frac{25}{441} as the division of square roots \frac{\sqrt{25}}{\sqrt{441}}. Take the square root of both numerator and denominator.

$$\frac{1}{25}\times \frac{5}{21}$$

Multiply \frac{1}{25} times \frac{5}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 5}{25\times 21}$$

Do the multiplications in the fraction \frac{1\times 5}{25\times 21}.

$$\frac{5}{525}$$

Reduce the fraction \frac{5}{525} to lowest terms by extracting and canceling out 5.

$$\frac{1}{105}$$

Factor

$$\frac{1}{3 \cdot 5 \cdot 7} = 0.009523809523809525$$