Solve 6/5sqrt{250}div1/7sqrt{490}

$$\frac { 6 } { 5 } \sqrt { 250 } \div \frac { 1 } { 7 } \sqrt { 490 }$$

Evaluate

$$2940$$

Solution Steps

Factor 250=5^{2}\times 10. Rewrite the square root of the product \sqrt{5^{2}\times 10} as the product of square roots \sqrt{5^{2}}\sqrt{10}. Take the square root of 5^{2}.

$$\frac{\frac{6}{5}\times 5\sqrt{10}}{\frac{1}{7}}\sqrt{490}$$

Cancel out 5 and 5.

$$\frac{6\sqrt{10}}{\frac{1}{7}}\sqrt{490}$$

Divide 6\sqrt{10} by \frac{1}{7} by multiplying 6\sqrt{10} by the reciprocal of \frac{1}{7}.

$$6\sqrt{10}\times 7\sqrt{490}$$

Multiply 6 and 7 to get 42.

$$42\sqrt{10}\sqrt{490}$$

Factor 490=7^{2}\times 10. Rewrite the square root of the product \sqrt{7^{2}\times 10} as the product of square roots \sqrt{7^{2}}\sqrt{10}. Take the square root of 7^{2}.

$$42\sqrt{10}\times 7\sqrt{10}$$

Multiply 42 and 7 to get 294.

$$294\sqrt{10}\sqrt{10}$$

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

$$294\times 10$$

Multiply 294 and 10 to get 2940.

$$2940$$

Factor

$$2^{2}\times 3\times 5\times 7^{2}$$