This lesson will show how to solve radical equations. If an equation has a variable in the radicand or a variable with a fractional exponent, we call the equation a radical equation. Study the easy example below.
If the index of the radical is 2, the equation is called square root equation.
To solve square root equations, isolate the radical on one side of the equation. Then, raise both sides of the equation to the same power.
$$ Trick: \ If \ \sqrt[n]{y} = c, then \ (\sqrt[n]{y})^n = c^n \ and \ y = c^n $$ |
$$ 4 + \sqrt{3x-2} = 6 $$ |
Isolate the radical on one side of the equation
$$ 4 - 4 + \sqrt{3x-2} = 6 - 4 $$ |
$$ \sqrt{3x-2} = 2 $$ |
Since you are dealing with a square root equation, raise both sides of the equation to the second power.
$$ (\sqrt{3x-2})^2 = 2^2 $$ |
3x - 2 = 4
3x - 2 + 2 = 4 + 2
3x = 6
x = 2
To solve equations with two radical expressions, isolate one of the radicals.
Isolate one radical
Raise both sides to the 4th power
Apr 02, 20 12:05 PM
Find out how to become an operations research analyst if you have a math major.
Basic math formulas
Algebra word problems
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.