Solve θ-7sqrt{8}div-6sqrt{8}

$$\theta - 7 \sqrt { 8 } \div - 6 \sqrt { 8 }$$

Evaluate

$$\theta +\frac{28}{3}$$

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}.

$$\theta -\frac{7\times 2\sqrt{2}}{-6}\sqrt{8}$$

Multiply 7 and 2 to get 14.

$$\theta -\frac{14\sqrt{2}}{-6}\sqrt{8}$$

Divide 14\sqrt{2} by -6 to get -\frac{7}{3}\sqrt{2}.

$$\theta -\left(-\frac{7}{3}\sqrt{2}\sqrt{8}\right)$$

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}.

$$\theta -\left(-\frac{7}{3}\sqrt{2}\times 2\sqrt{2}\right)$$

Express -\frac{7}{3}\times 2 as a single fraction.

$$\theta -\frac{-7\times 2}{3}\sqrt{2}\sqrt{2}$$

Multiply -7 and 2 to get -14.

$$\theta -\frac{-14}{3}\sqrt{2}\sqrt{2}$$

Fraction \frac{-14}{3} can be rewritten as -\frac{14}{3} by extracting the negative sign.

$$\theta -\left(-\frac{14}{3}\sqrt{2}\sqrt{2}\right)$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\theta -\left(-\frac{14}{3}\times 2\right)$$

Express -\frac{14}{3}\times 2 as a single fraction.

$$\theta -\frac{-14\times 2}{3}$$

Multiply -14 and 2 to get -28.

$$\theta -\frac{-28}{3}$$

Fraction \frac{-28}{3} can be rewritten as -\frac{28}{3} by extracting the negative sign.

$$\theta -\left(-\frac{28}{3}\right)$$

The opposite of -\frac{28}{3} is \frac{28}{3}.

$$\theta +\frac{28}{3}$$

Factor

$$\frac{3\theta +28}{3}$$

Solution Steps

Factor out \frac{1}{6}.

$$\frac{6\theta +28\left(\sqrt{2}\right)^{2}}{6}$$

Consider 6\theta +56. Factor out 2.

$$2\left(3\theta +28\right)$$

Rewrite the complete factored expression.

$$\frac{3\theta +28}{3}$$