A radical equation is an equation that involves a root.

x = 5

There are various methods to solve a radical equation; let's examine each.

Graphical approach

To solve a radical equation graphically, you have to draw the left-hand and right-hand side of the equation as individual graphs.

x = 5 f (x) = x and g (x) = 5

By identifying the

x -

value where these graphs intersect, we can solve the equation. This assumes that the solution is a whole number.

Numerical approach

Another way of solving a radical equation is by applying a numerical approach. This means we systematically try numbers until we get a solution or, at least, an approximate solution.

$x$	$x$	=
$23$	$23$	$\approx 4.79$
$24$	$24$	$\approx 4.90$
$25$	$25$	$5$

For more difficult radical equations, we should use a spreadsheet.

Analytical approach

The analytical approach is another way of saying algebraic approach. This means that you use inverse operations to solve for

x .

For radical equations, this involves isolating the radical and then raising both sides of the equation to the same exponent as the radicals index, which then eliminates the radical.

(x)^{2} = 5^{2} \Leftrightarrow x = 25

Exercise