### About Radical Equations:

When we solve an equation with square roots involved, we isolate a square root, square both sides, and simplify. When square roots remain, we repeat this process until none are left. Once we are done, we solve the equation and check every solution in the original equation.

Test Objectives

- Demonstrate the ability to isolate a radical on one side of the equation
- Demonstrate the ability to use the squaring property of equality to eliminate square roots from an equation
- Demonstrate the ability to check all proposed solutions in the original equation

#1:

Instructions: Solve each equation.

a) $$2 =\sqrt{\frac{x}{4}}$$

b) $$k = \sqrt{-30 + 13k}$$

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#2:

Instructions: Solve each equation.

a) $$\sqrt{-x + 10} = x - 8$$

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#3:

Instructions: Solve each equation.

a) $$n - 8 = \sqrt{24 - 3n}$$

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#4:

Instructions: Solve each equation.

a) $$\sqrt{2n + 6} = 2 + \sqrt{9 - n}$$

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#5:

Instructions: Solve each equation.

a) $$4 - \sqrt{-4 - 4x} = \sqrt{-10 - 2x}$$

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Written Solutions:

#1:

Solutions:

a) $$x = 16$$

b) $$k = 10$$ or $$k = 3$$

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#2:

Solutions:

a) $$x = 9$$

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#3:

Solutions:

a) $$n = 8$$

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#4:

Solutions:

a) $$n = 5$$

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#5:

Solutions:

a) $$x = -5$$