Solve sqrt{6}*sqrt{3}:sqrt{2}-sqrt{2}*(sqrt{13}+sqrt{8})=

$$\sqrt { 6 } \cdot \sqrt { 3 } : \sqrt { 2 } - \sqrt { 2 } \cdot ( \sqrt { 13 } + \sqrt { 8 } ) =$$

Evaluate

$$-\sqrt{26}-1\approx -6.099019514$$

Solution Steps

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

$$\frac{\sqrt{3}\sqrt{2}\sqrt{3}}{\sqrt{2}}-\sqrt{2}\left(\sqrt{13}+\sqrt{8}\right)$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{3\sqrt{2}}{\sqrt{2}}-\sqrt{2}\left(\sqrt{13}+\sqrt{8}\right)$$

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

$$\frac{3\sqrt{2}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-\sqrt{2}\left(\sqrt{13}+\sqrt{8}\right)$$

The square of \sqrt{2} is 2.

$$\frac{3\sqrt{2}\sqrt{2}}{2}-\sqrt{2}\left(\sqrt{13}+\sqrt{8}\right)$$

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

$$\frac{3\times 2}{2}-\sqrt{2}\left(\sqrt{13}+\sqrt{8}\right)$$

Multiply 3 and 2 to get 6.

$$\frac{6}{2}-\sqrt{2}\left(\sqrt{13}+\sqrt{8}\right)$$

Divide 6 by 2 to get 3.

$$3-\sqrt{2}\left(\sqrt{13}+\sqrt{8}\right)$$

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}.

$$3-\sqrt{2}\left(\sqrt{13}+2\sqrt{2}\right)$$

Use the distributive property to multiply \sqrt{2} by \sqrt{13}+2\sqrt{2}.

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

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

$$3-\left(\sqrt{26}+2\left(\sqrt{2}\right)^{2}\right)$$

The square of \sqrt{2} is 2.

$$3-\left(\sqrt{26}+2\times 2\right)$$

Multiply 2 and 2 to get 4.

$$3-\left(\sqrt{26}+4\right)$$

To find the opposite of \sqrt{26}+4, find the opposite of each term.

$$3-\sqrt{26}-4$$

Subtract 4 from 3 to get -1.

$$-1-\sqrt{26}$$

Factor

$$-\sqrt{26}-1$$