Solve -2sqrt{13}div(-3sqrt{8})

$$- 2 \sqrt { 13 } \div ( - 3 \sqrt { 8 } )$$

Evaluate

$$\frac{\sqrt{26}}{6}\approx 0.849836586$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{-2\sqrt{13}}{-3\times 2\sqrt{2}}$$

Multiply -3 and 2 to get -6.

$$\frac{-2\sqrt{13}}{-6\sqrt{2}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-\sqrt{13}}{-3\sqrt{2}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{\sqrt{13}}{3\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{13}}{3\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{13}\sqrt{2}}{3\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{13}\sqrt{2}}{3\times 2}$$

To multiply \sqrt{13} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{26}}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$\frac{\sqrt{26}}{6}$$