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Radicals - Adding and Subtracting from Simplified (Values and Variables) (Level 4)

This math topic focuses on the skills of adding and subtracting radicals that include both numerical and algebraic expressions. The questions involve operations with square roots and cube roots, integrating variables and exponents into the expressions. The complexity of the problems ranges from basic manipulation of similar radicals to more complicated scenarios involving different indices and mixed terms. Each question provides multiple-choice answers, allowing learners to practice and verify their understanding of radical operations in algebra.

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

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Adding and Subtracting from Simplified (Values and Variables)

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

Add or subtract the radical expressions

3113+3p11b23−4p11bp33\sqrt[3]{11} + 3p\sqrt[3]{11{b}^{2}} - 4p\sqrt[3]{11bp}

Radicals - Adding and Subtracting from Simplified (Values and Variables) Worksheet

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Math worksheet on 'Radicals - Adding and Subtracting from Simplified (Values and Variables) (Level 4)'. Part of a broader unit on 'Radicals - Addition and Subtraction Intro' Learn online: app.mobius.academy/math/units/radicals_addition_and_subtraction_intro/
1
Add or subtract the radical expressions
A LaTex expression showing 5dsquare root of 11 - 4dsquare root of 11 + 3bsquare root of 11d
a A LaTex expression showing 5dsquare root of 11 - 3bsquare root of 11d
b A LaTex expression showing dsquare root of 11 - 3bsquare root of 11d
c A LaTex expression showing {d} to the power of -1 square root of 11 - 3bsquare root of 11d
d A LaTex expression showing 7{d} to the power of 2 square root of 13 - 4{d} to the power of 2 square root of 8 + 5bsquare root of 9{d to the power of 2 }
e A LaTex expression showing 7{d} to the power of 2 square root of 11 - 7dsquare root of 14 + 4bsquare root of 9{d to the power of 3 }
f A LaTex expression showing {d} to the power of 3 square root of 11 - 3bsquare root of 11d
2
Add or subtract the radical expressions
A LaTex expression showing 2{n} to the power of 2 rsquare root of 2 + 3{n} to the power of 2 square root of 2 + 5n{r} to the power of 2 square root of 2n
a A LaTex expression showing 4n{r} to the power of 3 + 5{n} to the power of 2 square root of 3 + 8n{r} to the power of 2 square root of 3n
b A LaTex expression showing 4{n} to the power of 2 rsquare root of 5 + 2nsquare root of 2 + 8nrsquare root of 4{n to the power of 3 }
c A LaTex expression showing 2{n} to the power of 2 rsquare root of 2 + 3{n} to the power of 2 square root of 2 + 5n{r} to the power of 2 square root of 2n
d A LaTex expression showing n{r} to the power of 3 + 2{n} to the power of 4 square root of 2 + {n} to the power of 2 {r} to the power of 4 square root of n
e A LaTex expression showing 3{n} to the power of 2 r + 2n + 6n{r} to the power of 2 square root of 2n
f A LaTex expression showing 5{n} to the power of 3 r + 4{n} to the power of 3 + 5{n} to the power of 3 {r} to the power of 3 square root of {n to the power of 2 }
3
Add or subtract the radical expressions
A LaTex expression showing 3xsquare root of 2 + 4square root of 2x + 4csquare root of 2c
a A LaTex expression showing xsquare root of 4 + 2square root of 4x + 6{c} to the power of 3 square root of c
b A LaTex expression showing {x} to the power of 3 + 3square root of {x to the power of 2 } + csquare root of c
c A LaTex expression showing 5x + 3square root of {x to the power of 2 } + 6{c} to the power of 2 square root of {c to the power of 3 }
d A LaTex expression showing x + 2square root of 5x + 6csquare root of 4c
e A LaTex expression showing x + square root of x + 7csquare root of 2c
f A LaTex expression showing 3xsquare root of 2 + 4square root of 2x + 4csquare root of 2c
4
Add or subtract the radical expressions
A LaTex expression showing 3m3-th root of 3m + 2md3-th root of 3d - 2m3-th root of 3m
a A LaTex expression showing 4m3-th root of 2m + md3-th root of 6d - {m} to the power of 2 3-th root of m
b A LaTex expression showing m3-th root of m + 2md3-th root of 3d
c A LaTex expression showing m3-th root of 3m + 2md3-th root of 3d
d A LaTex expression showing m3-th root of 3 + 2md3-th root of 3d
e A LaTex expression showing {m} to the power of 3 3-th root of 3m + 2md3-th root of 3d
f A LaTex expression showing m3-th root of 4m + 2md3-th root of 3d
5
Add or subtract the radical expressions
A LaTex expression showing 2m3-th root of 3{p to the power of 2 m} - 4m3-th root of 3 - 3p3-th root of 3pm
a A LaTex expression showing 2m3-th root of 3{p to the power of 2 m} - 4m3-th root of 3 - 3p3-th root of 3pm
b A LaTex expression showing 4{m} to the power of 2 3-th root of 3{p to the power of 2 m} - m3-th root of 3 - 6p3-th root of 5pm
c A LaTex expression showing 4m3-th root of pm - 4m - 6p3-th root of 2pm
d A LaTex expression showing {m} to the power of 2 3-th root of 3{p to the power of 2 m} - 6m - 3p3-th root of p{m to the power of 3 }
e A LaTex expression showing 4m3-th root of p{m to the power of 2 } - {m} to the power of 3 - 4{p} to the power of 2 3-th root of {p to the power of 2 {m} to the power of 3 }
f A LaTex expression showing m3-th root of {p to the power of 4 m} - {m} to the power of 2 - p3-th root of 3{p to the power of 2 m}
6
Add or subtract the radical expressions
A LaTex expression showing 43-th root of 5n + 33-th root of 5n - 4c3-th root of 5{n to the power of 2 }
a A LaTex expression showing 73-th root of n + 4c3-th root of 5{n to the power of 2 }
b A LaTex expression showing 73-th root of 5{n to the power of 3 } + 4c3-th root of 5{n to the power of 2 }
c A LaTex expression showing 73-th root of 5 + 4c3-th root of 5{n to the power of 2 }
d A LaTex expression showing 73-th root of 5n + 4c3-th root of 5{n to the power of 2 }
e A LaTex expression showing 73-th root of 5{n to the power of -1 } + 4c3-th root of 5{n to the power of 2 }
f A LaTex expression showing 73-th root of 5{n to the power of 2 } + 4c3-th root of 5{n to the power of 2 }
7
Add or subtract the radical expressions
A LaTex expression showing 4b3-th root of 3b + 4x3-th root of 3{b to the power of 2 x} + 33-th root of 3b
a A LaTex expression showing b3-th root of 5b + 5x3-th root of bx + 63-th root of 3b
b A LaTex expression showing 4{b} to the power of 2 3-th root of 6{b to the power of 2 } + 6x3-th root of bx + 3-th root of 5{b to the power of 3 }
c A LaTex expression showing 7{b} to the power of 2 3-th root of 4b + x3-th root of 6{b to the power of 3 {x} to the power of 2 } + 53-th root of {b to the power of 3 }
d A LaTex expression showing 2{b} to the power of 3 3-th root of 5{b to the power of 3 } + 7x3-th root of 3{b to the power of 2 x} + 23-th root of 2b
e A LaTex expression showing 2b3-th root of {b to the power of 3 } + 4x3-th root of {b to the power of 2 {x} to the power of 3 } + 43-th root of 3{b to the power of 2 }
f A LaTex expression showing 4b3-th root of 3b + 4x3-th root of 3{b to the power of 2 x} + 33-th root of 3b