Solve -5sqrt{3}+sqrt{{left(5sqrt{3}right)}^2-4*4*3}

$$-5 \sqrt{ 3 } + \sqrt{ { \left(5 \sqrt{ 3 } \right) }^{ 2 } -4 \times 4 \times 3 }$$

Evaluate

$$-2\sqrt{3}\approx -3.464101615$$

Solution Steps

Expand \left(5\sqrt{3}\right)^{2}.

$$-5\sqrt{3}+\sqrt{5^{2}\left(\sqrt{3}\right)^{2}-4\times 4\times 3}$$

Calculate 5 to the power of 2 and get 25.

$$-5\sqrt{3}+\sqrt{25\left(\sqrt{3}\right)^{2}-4\times 4\times 3}$$

The square of \sqrt{3} is 3.

$$-5\sqrt{3}+\sqrt{25\times 3-4\times 4\times 3}$$

Multiply 25 and 3 to get 75.

$$-5\sqrt{3}+\sqrt{75-4\times 4\times 3}$$

Multiply 4 and 4 to get 16.

$$-5\sqrt{3}+\sqrt{75-16\times 3}$$

Multiply 16 and 3 to get 48.

$$-5\sqrt{3}+\sqrt{75-48}$$

Subtract 48 from 75 to get 27.

$$-5\sqrt{3}+\sqrt{27}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$-5\sqrt{3}+3\sqrt{3}$$

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

$$-2\sqrt{3}$$