Solving Radical Equations

Front

What is a radical equation?

Back

A radical equation is an equation in which a variable is contained within a radical (square root, cube root, etc.).

Tags

CCSS.HSA.REI.A.2

Front

How do you isolate a variable in a radical equation?

Back

To isolate a variable in a radical equation, you can square both sides of the equation to eliminate the radical, then solve for the variable.

Tags

CCSS.HSA.REI.A.2

Front

What is the first step in solving the equation √(x + 3) = 5?

Back

The first step is to square both sides of the equation: (√(x + 3))^2 = 5^2, which simplifies to x + 3 = 25.

Tags

CCSS.HSA.REI.A.2

Front

What must you do after squaring both sides of a radical equation?

Back

After squaring both sides, you must check for extraneous solutions by substituting back into the original equation.

Tags

CCSS.HSA.REI.A.2

Front

What is an extraneous solution?

Back

An extraneous solution is a solution that emerges from the process of solving the equation but does not satisfy the original equation.

Tags

CCSS.HSA.REI.A.2

Front

Solve the radical equation: √(2x + 1) = 3.

Back

Square both sides: 2x + 1 = 9. Then, solve for x: 2x = 8, so x = 4.

Tags

CCSS.HSA.REI.A.2

Front

What is the importance of checking solutions in radical equations?

Back

Checking solutions is important to ensure that the solutions found are valid and do not violate the original equation.

Tags

CCSS.HSA.REI.A.2

Front

How do you solve the equation √(x - 2) + 3 = 7?

Back

First, isolate the radical: √(x - 2) = 4. Then square both sides: x - 2 = 16, so x = 18.

Tags

CCSS.HSA.REI.A.2

Front

What is the general form of a radical equation?

Back

The general form of a radical equation can be expressed as √(f(x)) = g(x), where f(x) and g(x) are functions of x.

Tags

CCSS.HSA.REI.A.2

Front

What happens if you have a radical equation with multiple radicals?

Back

If there are multiple radicals, isolate one radical at a time, square both sides, and repeat the process until all radicals are eliminated.

Tags

CCSS.HSA.REI.A.2