Solve sqrt{28}*(-1)-sqrt{28}*sqrt{7}

$$\sqrt { 28 } \cdot ( - 1 ) - \sqrt { 28 } \cdot \sqrt { 7 }$$

Evaluate

$$-2\sqrt{7}-14\approx -19.291502622$$

Solution Steps

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$2\sqrt{7}\left(-1\right)-\sqrt{28}\sqrt{7}$$

Multiply 2 and -1 to get -2.

$$-2\sqrt{7}-\sqrt{28}\sqrt{7}$$

Factor 28=7\times 4. Rewrite the square root of the product \sqrt{7\times 4} as the product of square roots \sqrt{7}\sqrt{4}.

$$-2\sqrt{7}-\sqrt{7}\sqrt{4}\sqrt{7}$$

Multiply \sqrt{7} and \sqrt{7} to get 7.

$$-2\sqrt{7}-7\sqrt{4}$$

Calculate the square root of 4 and get 2.

$$-2\sqrt{7}-7\times 2$$

Multiply 7 and 2 to get 14.

$$-2\sqrt{7}-14$$

Factor

$$2 {(-\sqrt{7} - 7)} = -19.291502622$$