Discuss graphical, numerical, and analytical methods of solving a radical.
See solution.
Practice makes perfect
A radical equation is an equation that involves a root.
sqrt(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.
sqrt(x)= 5 f(x)= sqrt(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
sqrt(x)
=
23
sqrt(23)
≈ 4.79
24
sqrt(24)
≈ 4.90
25
sqrt(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.
(sqrt(x))^2=5^2 ⇔ x=25
