Grade 11 · Math · Algebra 2

11th grade Nth roots, and simplify, multiply, add and rationalize radicals worksheet

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nth roots, and simplify, multiply, add and rationalize radicals

Grade 11 Math Worksheet - Challenge Me

NameDate

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

1.
Bo clears the root from the bottom of 4/(3 − √5) for a math club card. Which is 4/(3 − √5) with a whole-number bottom?
- (6 + 2√5)/7
- 1
- 3 − √5
- 3 + √5
2.
Esme's robot shows 9/(√7 + 2) and needs a whole-number bottom. Which is 9/(√7 + 2) with a whole-number bottom?
- 3
- (9√7 − 18)/11
- 3√7 + 6
- 3√7 − 6
3.
Jun's math book asks to rationalize 2/(√5 + √3). Which is 2/(√5 + √3) with a whole-number bottom?
- √5 − √3
- √5 + √3
- (√5 − √3)/4
- 1
4.
Milo's math book shows √(75x⁵), for x ≥ 0. Which is √(75x⁵) fully simplified?
- 5x²√3
- 5x²√(3x)
- 25x⁴√(3x)
Noah divides ∛(81x⁵) ÷ ∛(3x²) for x > 0 on the class board. What is the quotient as one term?
Pia's robot divides ∜(48x⁷) ÷ ∜(3x³) for x > 0. What is the quotient as one term?
Ren works out ⁵√(96x¹²) ÷ ⁵√(3x²) for x > 0 on a math club card. What is the quotient as one term?
Tala simplifies (16x⁸)^(3/4) for x ≥ 0 on a math club card. What is (16x⁸)^(3/4) as one term?
Zee's math book shows (27x⁶)^(2/3), for x ≥ 0. What is (27x⁶)^(2/3) as one term?
Ari's robot simplifies (32x¹⁵)^(2/5) for x ≥ 0. What is (32x¹⁵)^(2/5) as one term?

11th grade Nth roots, and simplify, multiply, add and rationalize radicals worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Nth roots, and simplify, multiply, add and rationalize radicals. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can find a 4th, 5th or 6th root by asking which number, used that many times, multiplies back.
I can switch between a root and a fraction power, and say when a root of a negative number is not real.
I can simplify, multiply, add and divide roots, and clear a root from the bottom of a fraction, using a conjugate when the bottom has two terms.

Words to know

index: The small number on a root: how many equal factors it asks for.

radicand: The number or term under the root sign.

nth root: The number that, used n times as a factor, gives the radicand.

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

like roots: Roots with the same index and the same number inside.

rationalize: Rewrite a fraction so no root is left in the bottom.

conjugate: The same two terms with the middle sign flipped: 3 − √5 and 3 + √5.

Common mistakes

Your child divided by the small number on the root instead of finding equal factors (∜16 written as 4).

Your child took a square root when the root asked for 4 or 6 equal factors.

Your child swapped the root and the power when changing between a root and a fraction power (∛(x²) written as x^(3/2)).

What to say

Ask: which number times itself 4 times makes 16?

Ask: how many equal factors does the small number on the root ask for?

Ask: which number tells how many equal factors?

Questions parents ask

What is the most common mistake with nth roots, and simplify, multiply, add and rationalize radicals?

Your child divided by the small number on the root instead of finding equal factors (∜16 written as 4).

How can I help my child with nth roots, and simplify, multiply, add and rationalize radicals?

Ask: which number times itself 4 times makes 16?

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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