SOLVING RADICAL EQUATIONS

• 'n' is the index and 'ax + b' is the radicand.

• 'n' is the radicand and 'ax + b' is the index.

• 'n' is the exponent and 'ax + b' is the base.

• 'n' is the coefficient and 'ax + b' is the variable.

What defines a radical equation?

• An equation where the variable is under a radical or has a rational exponent.

• An equation with only integer exponents.

• An equation that always results in an extraneous solution.

• An equation that contains only quadratic terms.

What is the initial step when solving radical equations?

• Isolate the radicals and identify the index.

• Raise both sides of the equation to the index of the radical.

• Apply algebraic techniques like factoring.

• Check your solutions for extraneous solutions.

Which statement accurately defines an extraneous solution?

• A solution of the transformed equation that does not satisfy the original equation.

• A solution that satisfies both the transformed and original equations.

• A solution found before applying algebraic techniques.

• A solution that only applies to linear equations.

What is an extraneous solution in the context of radical equations?

• A solution that satisfies the original equation but not the transformed equation.

• A solution that satisfies both the original and the transformed equation.

• A solution that satisfies the transformed equation but not the original equation.

• A solution that is always negative.

What is the solution for the equation √(x) = 5?

• x = 5

• x = 10

• x = 25

• x = -25

What is the value of x that satisfies the equation √(2x - 5) = 7?

• x = 22

• x = 27

• x = 32

• x = 37

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What is the solution for the equation √(4x + 1) - √(3x + 7) = 0?

• x = 4

• x = 5

• x = 6

• x = 7

After isolating one radical and squaring both sides, what is the resulting equation for the radical equation √4x + 1 - √3x + 7 = 0?

• 4x + 1 = 3x + 7

• (4x + 1)² = (3x + 7)²

• 4x + 1 - (3x + 7) = 0

• √4x + 1 = 3x + 7