Solve (sqrt{12}-sqrt{188}+sqrt{75})*sqrt{3}

$$( \sqrt { 12 } - \sqrt { 188 } + \sqrt { 75 } ) \cdot \sqrt { 3 }$$

Evaluate

$$21-2\sqrt{141}\approx -2.748684174$$

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}.

$$\left(2\sqrt{3}-\sqrt{188}+\sqrt{75}\right)\sqrt{3}$$

Factor 188=2^{2}\times 47. Rewrite the square root of the product \sqrt{2^{2}\times 47} as the product of square roots \sqrt{2^{2}}\sqrt{47}. Take the square root of 2^{2}.

$$\left(2\sqrt{3}-2\sqrt{47}+\sqrt{75}\right)\sqrt{3}$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$\left(2\sqrt{3}-2\sqrt{47}+5\sqrt{3}\right)\sqrt{3}$$

Combine 2\sqrt{3} and 5\sqrt{3} to get 7\sqrt{3}.

$$\left(7\sqrt{3}-2\sqrt{47}\right)\sqrt{3}$$

Use the distributive property to multiply 7\sqrt{3}-2\sqrt{47} by \sqrt{3}.

$$7\left(\sqrt{3}\right)^{2}-2\sqrt{47}\sqrt{3}$$

The square of \sqrt{3} is 3.

$$7\times 3-2\sqrt{47}\sqrt{3}$$

Multiply 7 and 3 to get 21.

$$21-2\sqrt{47}\sqrt{3}$$

To multiply \sqrt{47} and \sqrt{3}, multiply the numbers under the square root.

$$21-2\sqrt{141}$$