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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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 3c{x} to the power of 2 square root of 7c + 2csquare root of 7 - 5csquare root of 7
a A LaTex expression showing 3c{x} to the power of 2 square root of 7c - 3csquare root of 3
b A LaTex expression showing 3c{x} to the power of 2 square root of 7c - 3csquare root of 7
c A LaTex expression showing 3c{x} to the power of 2 square root of 7c - 3c
d A LaTex expression showing 3c{x} to the power of 2 square root of 7c + 4csquare root of 7
2
Add or subtract the radical expressions
A LaTex expression showing 23-th root of 2{n to the power of 2 r} + 3n3-th root of 2{r to the power of 2 } - 4nr3-th root of 2
a A LaTex expression showing 3-th root of {n to the power of 4 {r} to the power of 3 } + {n} to the power of 2 3-th root of {r to the power of 4 } - 5{n} to the power of 2 {r} to the power of 2
b A LaTex expression showing 23-th root of 2{n to the power of 2 r} + 3n3-th root of 2{r to the power of 2 } - 4nr3-th root of 2
c A LaTex expression showing 43-th root of nr + {n} to the power of 3 3-th root of 2{r to the power of 4 } - 3{n} to the power of 2 r3-th root of 5
d A LaTex expression showing 3-th root of 4{n to the power of 2 {r} to the power of 3 } + 4n3-th root of 5r - n{r} to the power of 3
3
Add or subtract the radical expressions
A LaTex expression showing 33-th root of 2z - 3z3-th root of 2{x to the power of 2 } + 4x3-th root of 2
a A LaTex expression showing 23-th root of z - z3-th root of {x to the power of 2 } + 4x
b A LaTex expression showing 33-th root of 2z - 3z3-th root of 2{x to the power of 2 } + 4x3-th root of 2
c A LaTex expression showing 33-th root of z - 2z3-th root of 2{x to the power of 3 } + x3-th root of 2
d A LaTex expression showing 3-th root of 2{z to the power of 2 } - 2z3-th root of 2{x to the power of 4 } + 6x3-th root of 3
4
Add or subtract the radical expressions
A LaTex expression showing 4{r} to the power of 2 square root of 7 - 3rsquare root of 7 - 2{z} to the power of 2 square root of 7r
a A LaTex expression showing rsquare root of 10 - 3rsquare root of 5 - {z} to the power of 3 square root of 9r
b A LaTex expression showing 4{r} to the power of 3 square root of 8 - 2rsquare root of 9 - zsquare root of 3r
c A LaTex expression showing rsquare root of 8 - 5rsquare root of 4 - 3zsquare root of 3r
d A LaTex expression showing 4{r} to the power of 2 square root of 7 - 3rsquare root of 7 - 2{z} to the power of 2 square root of 7r
5
Add or subtract the radical expressions
A LaTex expression showing 43-th root of 3{c to the power of 2 {d} to the power of 2 } - 23-th root of 3{d to the power of 2 } + 43-th root of 3{c to the power of 2 }
a A LaTex expression showing 43-th root of 2{c to the power of 3 d} - 3-th root of d + 73-th root of {c to the power of 3 }
b A LaTex expression showing 43-th root of 3{c to the power of 2 {d} to the power of 2 } - 23-th root of 3{d to the power of 2 } + 43-th root of 3{c to the power of 2 }
6
Add or subtract the radical expressions
A LaTex expression showing 3zsquare root of 11xz - 5xsquare root of 11xz - 5square root of 11
a A LaTex expression showing 2{z} to the power of 3 square root of 7{x to the power of 2 z} - 6xsquare root of 7{x to the power of 2 z} - 8square root of 11
b A LaTex expression showing 3zsquare root of 11xz - 5xsquare root of 11xz - 5square root of 11
c A LaTex expression showing 6{z} to the power of 3 square root of 10xz - 2{x} to the power of 2 square root of 14{x to the power of 3 z} - 5square root of 10
7
Add or subtract the radical expressions
A LaTex expression showing 2bn3-th root of 5 - 2n3-th root of 5bn + 4n3-th root of 5{b to the power of 2 }
a A LaTex expression showing bn3-th root of 3 - 3{n} to the power of 3 3-th root of 6{b to the power of 3 {n} to the power of 2 } + 4n3-th root of 6{b to the power of 3 }
b A LaTex expression showing 2bn3-th root of 5 - 2n3-th root of 5bn + 4n3-th root of 5{b to the power of 2 }
c A LaTex expression showing {b} to the power of 3 n3-th root of 5 - n3-th root of 6bn + 4{n} to the power of 3 3-th root of 3{b to the power of 2 }
d A LaTex expression showing b{n} to the power of 2 3-th root of 7 - {n} to the power of 3 3-th root of 2{b to the power of 3 n} + 5n3-th root of 5{b to the power of 3 }