Solve frac{-2sqrt{147}}{sqrt{3}}+20

$$\frac { - 2 \sqrt { 147 } } { \sqrt { 3 } } + 20$$

Evaluate

$$6$$

Solution Steps

Factor 147=7^{2}\times 3. Rewrite the square root of the product \sqrt{7^{2}\times 3} as the product of square roots \sqrt{7^{2}}\sqrt{3}. Take the square root of 7^{2}.

$$\frac{-2\times 7\sqrt{3}}{\sqrt{3}}+20$$

Multiply -2 and 7 to get -14.

$$\frac{-14\sqrt{3}}{\sqrt{3}}+20$$

Rationalize the denominator of \frac{-14\sqrt{3}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{-14\sqrt{3}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}+20$$

The square of \sqrt{3} is 3.

$$\frac{-14\sqrt{3}\sqrt{3}}{3}+20$$

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

$$\frac{-14\times 3}{3}+20$$

Multiply -14 and 3 to get -42.

$$\frac{-42}{3}+20$$

Divide -42 by 3 to get -14.

$$-14+20$$

Add -14 and 20 to get 6.

$$6$$

Factor

$$2\times 3$$