Solve 6-2sqrt{3}y-6/sqrt{3}sqrt{1-yy}

$$6-2 \sqrt{ 3 } y- \frac{ 6 }{ \sqrt{ 3 } } \sqrt{ 1-yy }$$

Factor

$$2\sqrt{3}\left(-\sqrt{1-y^{2}}-y+\sqrt{3}\right)$$

Solution Steps

Multiply y and y to get y^{2}.

$$factor(6-2\sqrt{3}y-\frac{6}{\sqrt{3}}\sqrt{1-y^{2}})$$

Rationalize the denominator of \frac{6}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$factor(6-2\sqrt{3}y-\frac{6\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\sqrt{1-y^{2}})$$

The square of \sqrt{3} is 3.

$$factor(6-2\sqrt{3}y-\frac{6\sqrt{3}}{3}\sqrt{1-y^{2}})$$

Divide 6\sqrt{3} by 3 to get 2\sqrt{3}.

$$factor(6-2\sqrt{3}y-2\sqrt{3}\sqrt{1-y^{2}})$$

Factor out 2.

$$2\left(3-\sqrt{3}y-\sqrt{3}\sqrt{1-y^{2}}\right)$$

Consider 3-\sqrt{3}y-\sqrt{3}\sqrt{1-y^{2}}. Factor out \sqrt{3}.

$$\sqrt{3}\left(\sqrt{3}-y-\sqrt{1-y^{2}}\right)$$

Rewrite the complete factored expression.

$$2\sqrt{3}\left(\sqrt{3}-y-\sqrt{1-y^{2}}\right)$$

Evaluate

$$-2\sqrt{3}y-2\sqrt{3-3y^{2}}+6$$