Solve x^2=(6+3sqrt{3})(8-4sqrt{3})

$$x ^ { 2 } = ( 6 + 3 \sqrt { 3 } ) ( 8 - 4 \sqrt { 3 } )$$

Solve for x

$$x=2\sqrt{3}\approx 3.464101615$$

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

Steps by Finding Square Root

Use the distributive property to multiply 6+3\sqrt{3} by 8-4\sqrt{3} and combine like terms.

$$x^{2}=48-12\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$x^{2}=48-12\times 3$$

Multiply -12 and 3 to get -36.

$$x^{2}=48-36$$

Subtract 36 from 48 to get 12.

$$x^{2}=12$$

Take the square root of both sides of the equation.

$$x=2\sqrt{3} x=-2\sqrt{3}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 6+3\sqrt{3} by 8-4\sqrt{3} and combine like terms.

$$x^{2}=48-12\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$x^{2}=48-12\times 3$$

Multiply -12 and 3 to get -36.

$$x^{2}=48-36$$

Subtract 36 from 48 to get 12.

$$x^{2}=12$$

Subtract 12 from both sides.

$$x^{2}-12=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-12\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-12\right)}}{2}$$

Multiply -4 times -12.

$$x=\frac{0±\sqrt{48}}{2}$$

Take the square root of 48.

$$x=\frac{0±4\sqrt{3}}{2}$$

Now solve the equation x=\frac{0±4\sqrt{3}}{2} when ± is plus.

$$x=2\sqrt{3}$$

Now solve the equation x=\frac{0±4\sqrt{3}}{2} when ± is minus.

$$x=-2\sqrt{3}$$

The equation is now solved.

$$x=2\sqrt{3} x=-2\sqrt{3}$$