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Radicals - Cube - Simplify From Cubed Factors, Values and Variables, Nothing Remaining (Level 3)

This math topic focuses on simplifying cube radicals with various cubed factors, constants, and variables, ensuring that no factors remain inside the radical upon simplification. The problems escalate in complexity and teach students to simplify expressions featuring powers and coefficients, helping them understand and manipulate radical terms effectively. Each question provides multiple-choice answers, allowing students to practice and confirm their understanding of the procedures involved in radical simplification at an advanced level.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Cube - Simplify From Cubed Factors, Values and Variables, Nothing Remaining

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Simplify the radical

22⋅22⋅p2⋅p2⋅b2⋅\sqrt{2^2\cdot 2^2\cdot p^2\cdot p^2\cdot b^2\cdot }

Radicals - Cube - Simplify From Cubed Factors, Values and Variables, Nothing Remaining Worksheet

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Math worksheet on 'Radicals - Cube - Simplify From Cubed Factors, Values and Variables, Nothing Remaining (Level 3)'. Part of a broader unit on 'Radicals - Simplifying Advanced' Learn online: app.mobius.academy/math/units/radicals_simplifying_advanced/
1
Simplify the radical
A LaTex expression showing square root of 3 to the power of 2 times x to the power of 2 times y to the power of 2 times y to the power of 2 times
a A LaTex expression showing 5{x} to the power of 3 {y} to the power of 2
b A LaTex expression showing 3x{y} to the power of 2
c A LaTex expression showing 3{x} to the power of 3 {y} to the power of 4
d A LaTex expression showing 3x{y} to the power of 3
e A LaTex expression showing 2{x} to the power of 3 y
f A LaTex expression showing x{y} to the power of 2
2
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times 2 to the power of 2 times p to the power of 2 times p to the power of 2 times b to the power of 2 times
a A LaTex expression showing 4{p} to the power of 4 {b} to the power of 3
b A LaTex expression showing 5p{b} to the power of 3 square root of 3
c A LaTex expression showing 6{p} to the power of 3 b
d A LaTex expression showing {p} to the power of 2 bsquare root of 3
e A LaTex expression showing 5{p} to the power of 3 {b} to the power of 2
f A LaTex expression showing 4{p} to the power of 2 b
3
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times m to the power of 2 times m to the power of 2 times b to the power of 2 times b to the power of 2 times
a A LaTex expression showing m{b} to the power of 3
b A LaTex expression showing m{b} to the power of 3 square root of 4
c A LaTex expression showing 3{m} to the power of 2 b
d A LaTex expression showing {m} to the power of 2 {b} to the power of 2 square root of 2
e A LaTex expression showing 2{m} to the power of 2 {b} to the power of 2
f A LaTex expression showing 3mbsquare root of 3
4
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times m to the power of 2 times m to the power of 2 times z to the power of 2 times
a A LaTex expression showing 2{m} to the power of 2 z
b A LaTex expression showing 3{m} to the power of 3 z
c A LaTex expression showing {m} to the power of 2 z
d A LaTex expression showing 3{m} to the power of 3 {z} to the power of 2 square root of 3
e A LaTex expression showing 3m{z} to the power of 2 square root of 3
f A LaTex expression showing {m} to the power of 3 {z} to the power of 2 square root of 3
5
Simplify the radical
A LaTex expression showing square root of 3 to the power of 2 times m to the power of 2 times m to the power of 2 times d to the power of 2 times
a A LaTex expression showing 5m{d} to the power of 3
b A LaTex expression showing {m} to the power of 3 {d} to the power of 3
c A LaTex expression showing 3{m} to the power of 2 d
d A LaTex expression showing 5{m} to the power of 2 dsquare root of 4
e A LaTex expression showing 4{m} to the power of 3 dsquare root of 4
f A LaTex expression showing {m} to the power of 4 dsquare root of 2
6
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times 2 to the power of 2 times n to the power of 2 times n to the power of 2 times b to the power of 2 times b to the power of 2 times
a A LaTex expression showing 7n{b} to the power of 3 square root of 2
b A LaTex expression showing 5{n} to the power of 2 bsquare root of 4
c A LaTex expression showing 3{n} to the power of 4 bsquare root of 4
d A LaTex expression showing 5{n} to the power of 2 bsquare root of 2
e A LaTex expression showing 6nbsquare root of 4
f A LaTex expression showing 4{n} to the power of 2 {b} to the power of 2
7
Simplify the radical
A LaTex expression showing square root of 3 to the power of 2 times b to the power of 2 times b to the power of 2 times d to the power of 2 times d to the power of 2 times
a A LaTex expression showing 6{b} to the power of 4 dsquare root of 3
b A LaTex expression showing 4{b} to the power of 4 {d} to the power of 3
c A LaTex expression showing 4{b} to the power of 3 dsquare root of 4
d A LaTex expression showing 4bdsquare root of 3
e A LaTex expression showing 6{b} to the power of 4 {d} to the power of 4 square root of 2
f A LaTex expression showing 3{b} to the power of 2 {d} to the power of 2