Grade 11 · Math · Algebra 2

11th grade Solve radical equations and equations with rational exponents, and check for fake answers worksheet

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Solve radical equations and equations with rational exponents, and check for fake answers

Grade 11 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

Noah solves √(x² + 64) = 17 for x > 0 on a math club card. What is x?
Pia's robot solves √(x² + 81) = 15 for x > 0. What is x?
Ren solves √(x² + 576) = 25 for x > 0 in a math book. What is x?
A ball falls h feet in t = √h ÷ 4 seconds. Zee drops a play ball from the top bleacher in science class; the fall takes 0.75 seconds. How many feet did it fall?
5.
Bo solves √(x + 2) + 4 = x on a math club card and checks each answer. Which choice gives every solution?
- x = 7 only
- no solution
- x = 7 and x = 2
- x = 2 only
6.
Esme's robot solves √(2x + 7) + 4 = x and checks each answer. Which choice gives every solution?
- x = 9 only
- x = 9 and x = 1
- no solution
- x = 1 only
7.
Jun solves √(5x + 6) − 2 = x on the class board and checks each answer. Which choice gives every solution?
- x = -1 only
- x = 2 only
- no solution, both answers fail
- x = 2 and x = -1
Luz solves 2(x + 2)^(3/2) = 54 for a math club puzzle. What is x?
Milo's robot solves 3(x − 1)^(3/4) = 24. What is x?
Noah solves (x − 3)^(3/2) + 2 = 66 in a math book. What is x?

11th grade Solve radical equations and equations with rational exponents, and check for fake answers worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Solve radical equations and equations with rational exponents, and check for fake answers. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can undo a square root or cube root by building its strip back: square or cube both sides.
I can get the root alone first, then undo it, and solve x^(m/n) = c by raising both sides to n/m.
I can put every answer back into the first equation and keep only the ones that work.

Standard: A-REI.A.2, N-RN.A.2

Words to know

radical equation: An equation with x under a root sign.

square both sides: Multiply each side by itself to undo a square root.

isolate: Get the root alone on one side before undoing it.

fake answer (extraneous): An answer of the squared equation that fails in the first one.

check: Put the answer back into the first equation and compare both sides.

fraction power: x^(m/n): the nth root of x, taken m times.

Common mistakes

Your child solved the inside of a root as if the root were not there (√(x + 5) = 4 solved as x + 5 = 4).

Your child multiplied by 2 or 3 to undo a root instead of squaring or cubing (√(x + 5) = 4 turned into x + 5 = 8).

Your child added a number that should be subtracted (or the other way) when getting x alone.

What to say

Ask: if √(x + 5) = 4, what must x + 5 be?

Ask: is 4 squared 8 or 16?

Ask: what undoes + 5?

Questions parents ask

What is the most common mistake with solve radical equations and equations with rational exponents, and check for fake answers?

Your child solved the inside of a root as if the root were not there (√(x + 5) = 4 solved as x + 5 = 4).

How can I help my child with solve radical equations and equations with rational exponents, and check for fake answers?

Ask: if √(x + 5) = 4, what must x + 5 be?

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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