Solve sqrt{90/42*9}=

$$\sqrt { \frac { 90 } { 42 } \cdot 9 } =$$

Evaluate

$$\frac{3\sqrt{105}}{7}\approx 4.391550328$$

Solution Steps

Reduce the fraction \frac{90}{42} to lowest terms by extracting and canceling out 6.

$$\sqrt{\frac{15}{7}\times 9}$$

Express \frac{15}{7}\times 9 as a single fraction.

$$\sqrt{\frac{15\times 9}{7}}$$

Multiply 15 and 9 to get 135.

$$\sqrt{\frac{135}{7}}$$

Rewrite the square root of the division \sqrt{\frac{135}{7}} as the division of square roots \frac{\sqrt{135}}{\sqrt{7}}.

$$\frac{\sqrt{135}}{\sqrt{7}}$$

Factor 135=3^{2}\times 15. Rewrite the square root of the product \sqrt{3^{2}\times 15} as the product of square roots \sqrt{3^{2}}\sqrt{15}. Take the square root of 3^{2}.

$$\frac{3\sqrt{15}}{\sqrt{7}}$$

Rationalize the denominator of \frac{3\sqrt{15}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{3\sqrt{15}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{3\sqrt{15}\sqrt{7}}{7}$$

To multiply \sqrt{15} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{3\sqrt{105}}{7}$$