Lesson 5: 5-6 Solving Radical Equations

What are two ways to know that there are no real solutions to a radical equation?
Why does the square root of a number have two solutions?
Describe what the graph of a square root function usually looks like.

radical equation
extraneous solution
radical inequality

A.REI.2 Solve simple rational and radical equations in one variable and give examples showing how extraneous solutions may arise

See below

It is always important to check the solutions to an equation or inequality in the original equation, but it is especially important when both sides of an equation are raised to a power. If a solution is an approximation, it is sometime difficult to determine whether a discrepancy is due to rounding or if it an incorrect solution. Students should check exact solutions whenever possible.

When you jump, the time that youa re in the air is your hang time. Hang time can be calculated in seconds t if you know the height h of the jump in feet. The formula for hang time is t=.5h^(1/2). A volleyball player had a hange tie of about .67 seconds, how would you calculate the height of her jump?

Make sure that students know the constraints on the values of the variables in a radical equation so that the solutions are real numbers

Ask students to work in groups as they compare solving radical equations and inequalities to solving other types of equations and inequalities. Have them write or give a short presentation about the similarities and differences between the procedures used in the solution process

Use McGraw Hill resources

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