Solve sqrt{2}-sqrt{12}div1/2sqrt{50}*2sqrt{3/4}

$$\sqrt { 2 } - \sqrt { 12 } \div \frac { 1 } { 2 } \sqrt { 50 } \times 2 \sqrt { \frac { 3 } { 4 } }$$

Evaluate

$$-59\sqrt{2}\approx -83.43860018$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\sqrt{2}-2\times \frac{2\sqrt{3}}{\frac{1}{2}}\sqrt{50}\sqrt{\frac{3}{4}}$$

Divide 2\sqrt{3} by \frac{1}{2} by multiplying 2\sqrt{3} by the reciprocal of \frac{1}{2}.

$$\sqrt{2}-2\times 2\sqrt{3}\times 2\sqrt{50}\sqrt{\frac{3}{4}}$$

Multiply 2 and 2 to get 4.

$$\sqrt{2}-2\times 4\sqrt{3}\sqrt{50}\sqrt{\frac{3}{4}}$$

Multiply 2 and 4 to get 8.

$$\sqrt{2}-8\sqrt{3}\sqrt{50}\sqrt{\frac{3}{4}}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$\sqrt{2}-8\sqrt{3}\times 5\sqrt{2}\sqrt{\frac{3}{4}}$$

Multiply 8 and 5 to get 40.

$$\sqrt{2}-40\sqrt{3}\sqrt{2}\sqrt{\frac{3}{4}}$$

Rewrite the square root of the division \sqrt{\frac{3}{4}} as the division of square roots \frac{\sqrt{3}}{\sqrt{4}}.

$$\sqrt{2}-40\sqrt{3}\sqrt{2}\times \frac{\sqrt{3}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\sqrt{2}-40\sqrt{3}\sqrt{2}\times \frac{\sqrt{3}}{2}$$

Cancel out 2, the greatest common factor in 40 and 2.

$$\sqrt{2}-20\sqrt{3}\sqrt{3}\sqrt{2}$$

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

$$\sqrt{2}-20\times 3\sqrt{2}$$

Multiply 20 and 3 to get 60.

$$\sqrt{2}-60\sqrt{2}$$

Combine \sqrt{2} and -60\sqrt{2} to get -59\sqrt{2}.

$$-59\sqrt{2}$$