Higher Roots

Cube roots and higher roots. In MathBound, the free Algebra I adventure game, Cube-Beet Bertha asks these problems, and the only way past is to solve them.

Part of Exponents and Exponential Functions: chapter 7 of the standard course.

Play this battle free

10 questions, no sign-up, nothing saved. Climbs from the basics to harder questions.

What you will practice

Evaluate Higher Roots. Evaluate the principal higher root of a positive perfect power integer.
Simplify Variable Roots. Simplify a higher odd root of a variable with an exponent matching the index.
Use the Product Property. Simplify a higher root of an integer by factoring out the largest perfect nth power.
Use the Quotient Property. Divide higher roots by combining them under a single radical and simplifying.
Add/Subtract Higher Roots. Add or subtract higher roots with identical indices and radicands by combining coefficients.

Worked examples

Made by the game’s own question engine. Try each one, then open its steps.

Example 1 · Evaluate Higher Roots

Simplify:

481

$3$
$12$
$81$
$20$

Show the worked steps

$3$ $to$ $the$ $power$ $4$ $is$ $81 .$
$So$ $the$ $4 t h$ $root$ $of$ $81$ $is$ $3 .$

Answer: $3$

Example 2 · Simplify Variable Roots

Simplify:

5 n^{10}

$n^{10}$
$2 n$
$n^{2}$
$n^{5}$

Show the worked steps

$n^{10} = (n^{2})^{5} .$
$So$ $the$ $5 t h$ $root$ $is$ $n^{2} .$

Answer: $n^{2}$

Example 3 · Use the Product Property

Write

433

as

a

single

radical.

$48$
$348$
$3192$
$312$

Show the worked steps

$4 = 364,$ $so$ $it$ $goes$ $inside$ $as$ $64 .$
$64 \cdot 3 = 192 : 3192 .$

Answer: $3192$

Where it is in your textbook

Textbook	Lessons
Standard course	7.3
Big Ideas Math Algebra 1	6.2, 10.2
Big Ideas Math Algebra 1 (2022)	6.2, 10.2
Carnegie Learning Algebra I	M3 1.2
CPM Core Connections Algebra	1.2.2, 7.2.1
CPS Skyline Algebra	1.9-1.10, 2.6-2.7
enVision Algebra 1	10-2
enVision Algebra 1 (2024)	10-2
Eureka Math Algebra I (EngageNY)	4.18
HMH Into Algebra 1	1.2, 20.4
Math Nation Algebra 1 (Florida B.E.S.T.)	1.4, 1.8, 1.9
OpenStax Elementary Algebra 2e	9.7
Pearson Algebra 1 Common Core	7-5
Reveal Algebra 1	8-4
SpringBoard Algebra 1	20

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