Solve frac{sqrt{35}}{sqrt{5}}*frac{sqrt{10}}{sqrt{70}}

$$\frac { \sqrt { 35 } } { \sqrt { 5 } } \cdot \frac { \sqrt { 10 } } { \sqrt { 70 } }$$

Evaluate

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Solution Steps

Rewrite the division of square roots \frac{\sqrt{35}}{\sqrt{5}} as the square root of the division \sqrt{\frac{35}{5}} and perform the division.

$$\sqrt{7}\times \frac{\sqrt{10}}{\sqrt{70}}$$

Rationalize the denominator of \frac{\sqrt{10}}{\sqrt{70}} by multiplying numerator and denominator by \sqrt{70}.

$$\sqrt{7}\times \frac{\sqrt{10}\sqrt{70}}{\left(\sqrt{70}\right)^{2}}$$

The square of \sqrt{70} is 70.

$$\sqrt{7}\times \frac{\sqrt{10}\sqrt{70}}{70}$$

Factor 70=10\times 7. Rewrite the square root of the product \sqrt{10\times 7} as the product of square roots \sqrt{10}\sqrt{7}.

$$\sqrt{7}\times \frac{\sqrt{10}\sqrt{10}\sqrt{7}}{70}$$

Multiply \sqrt{10} and \sqrt{10} to get 10.

$$\sqrt{7}\times \frac{10\sqrt{7}}{70}$$

Divide 10\sqrt{7} by 70 to get \frac{1}{7}\sqrt{7}.

$$\sqrt{7}\times \frac{1}{7}\sqrt{7}$$

Multiply \sqrt{7} and \sqrt{7} to get 7.

$$7\times \frac{1}{7}$$

Cancel out 7 and 7.

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Factor

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