Solve frac{3sqrt{11}}{2sqrt{98}}div5/7|22

$$\frac { 3 \sqrt { 11 } } { 2 \sqrt { 98 } } \div \frac { 5 } { 7 | 22 }$$

Evaluate

$$\frac{33\sqrt{22}}{10}\approx 15.478372007$$

Solution Steps

Divide \frac{3\sqrt{11}}{2\sqrt{98}} by \frac{5}{7|22|} by multiplying \frac{3\sqrt{11}}{2\sqrt{98}} by the reciprocal of \frac{5}{7|22|}.

$$\frac{3\sqrt{11}\times 7|22|}{2\sqrt{98}\times 5}$$

Multiply 3 and 7 to get 21.

$$\frac{21\sqrt{11}|22|}{2\sqrt{98}\times 5}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 22 is 22.

$$\frac{21\sqrt{11}\times 22}{2\sqrt{98}\times 5}$$

Multiply 21 and 22 to get 462.

$$\frac{462\sqrt{11}}{2\sqrt{98}\times 5}$$

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$\frac{462\sqrt{11}}{2\times 7\sqrt{2}\times 5}$$

Multiply 2 and 7 to get 14.

$$\frac{462\sqrt{11}}{14\sqrt{2}\times 5}$$

Multiply 14 and 5 to get 70.

$$\frac{462\sqrt{11}}{70\sqrt{2}}$$

Cancel out 14 in both numerator and denominator.

$$\frac{33\sqrt{11}}{5\sqrt{2}}$$

Rationalize the denominator of \frac{33\sqrt{11}}{5\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{33\sqrt{11}\sqrt{2}}{5\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{33\sqrt{11}\sqrt{2}}{5\times 2}$$

To multiply \sqrt{11} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{33\sqrt{22}}{5\times 2}$$

Multiply 5 and 2 to get 10.

$$\frac{33\sqrt{22}}{10}$$