Find the Roots (Zeros) (x- square root of 3)^2(x- square root of 7)

${(x - \sqrt{3})}^{2} (x - \sqrt{7})$

Set ${(x - \sqrt{3})}^{2} (x - \sqrt{7})$ equal to $0$ .

${(x - \sqrt{3})}^{2} (x - \sqrt{7}) = 0$

Solve for $x$ .

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

${(x - \sqrt{3})}^{2} = 0$

$x - \sqrt{7} = 0$

Set ${(x - \sqrt{3})}^{2}$ equal to $0$ and solve for $x$ .

Set ${(x - \sqrt{3})}^{2}$ equal to $0$ .

${(x - \sqrt{3})}^{2} = 0$

Solve ${(x - \sqrt{3})}^{2} = 0$ for $x$ .

Set the $x - \sqrt{3}$ equal to $0$ .

$x - \sqrt{3} = 0$

Add $\sqrt{3}$ to both sides of the equation.

$x = \sqrt{3}$

Set $x - \sqrt{7}$ equal to $0$ and solve for $x$ .

Set $x - \sqrt{7}$ equal to $0$ .

$x - \sqrt{7} = 0$

Add $\sqrt{7}$ to both sides of the equation.

$x = \sqrt{7}$

The final solution is all the values that make ${(x - \sqrt{3})}^{2} (x - \sqrt{7}) = 0$ true.

$x = \sqrt{3}, \sqrt{7}$

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{3}, \sqrt{7}$

Decimal Form:

$x = 1.73205080 \dots, 2.64575131 \dots$