Adding and Subtracting from Simplified (Values and Variables) (Level 5)

This math topic focuses on practicing how to add and subtract radical expressions that involve both numerical and algebraic values, including roots of different indices and powers of variables. The problems require simplifying and combining terms with similar radical components. Each question presents multiple-choice answers, requiring the student to select or verify the correct simplified form of the given radical expressions. This forms part of a larger introductory unit on addition and subtraction of radicals.

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 5)'. 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 4x{c} to the power of 2 square root of 2x - 2xcsquare root of 2x + 3csquare root of 2
a A LaTex expression showing 2xcsquare root of x - xcsquare root of {x to the power of 2 } + 5csquare root of 4
b A LaTex expression showing 4x{c} to the power of 2 square root of 2x - 2xcsquare root of 2x + 3csquare root of 2
c A LaTex expression showing 6xcsquare root of 3{x to the power of 3 } - xcsquare root of x + 4c
d A LaTex expression showing 7x{c} to the power of 2 square root of x - 3{x} to the power of 3 {c} to the power of 3 square root of 5x + csquare root of 3
2
Add or subtract the radical expressions
A LaTex expression showing 33-th root of 2rz - 23-th root of 2r{z to the power of 2 } - 33-th root of 2r
a A LaTex expression showing 53-th root of rz - 3-th root of 4{r to the power of 2 z} - 33-th root of {r to the power of 2 }
b A LaTex expression showing 3-th root of 4rz - 3-th root of 2{r to the power of 3 {z} to the power of 3 } - 3-th root of 5{r to the power of 2 }
c A LaTex expression showing 33-th root of 2rz - 23-th root of 2r{z to the power of 2 } - 33-th root of 2r
d A LaTex expression showing 63-th root of 4r{z to the power of 3 } - 23-th root of r{z to the power of 4 } - 3-th root of r
3
Add or subtract the radical expressions
A LaTex expression showing 4square root of 3 - 2{x} to the power of 2 nsquare root of 3 - 2{x} to the power of 2 {n} to the power of 2 square root of 3
a A LaTex expression showing 4square root of 3 - 2{x} to the power of 2 nsquare root of 3 - 2{x} to the power of 2 {n} to the power of 2 square root of 3
b A LaTex expression showing 3 - {x} to the power of 2 n - 5{x} to the power of 2 nsquare root of 5
c A LaTex expression showing 7square root of 4 - {x} to the power of 2 n - 2{x} to the power of 2 nsquare root of 2
d A LaTex expression showing 5square root of 3 - 2{x} to the power of 4 nsquare root of 4 - x{n} to the power of 3
4
A LaTex expression showing 3{n} to the power of 2 square root of 11 + 2{n} to the power of 2 square root of 11y + 2{n} to the power of 2 square root of 11y
Add or subtract the radical expressions
a A LaTex expression showing 3{n} to the power of 2 square root of 11 + 2{n} to the power of 2 square root of 11y
b A LaTex expression showing 3{n} to the power of 2 square root of 11 + 4{n} to the power of 4 square root of 11y
c A LaTex expression showing 3{n} to the power of 2 square root of 11 + 4{n} to the power of 2 square root of 11y
d A LaTex expression showing 3{n} to the power of 2 square root of 11 + 4square root of 11y
e A LaTex expression showing 3{n} to the power of 2 square root of 11 + 4{n} to the power of 2 square root of 11{y to the power of -1 }
5
Add or subtract the radical expressions
A LaTex expression showing 3x3-th root of 2r + 23-th root of 2x{r to the power of 2 } + 4r3-th root of 2r
a A LaTex expression showing {x} to the power of 3 3-th root of 2r + 53-th root of {x to the power of 2 {r} to the power of 3 } + r3-th root of r
b A LaTex expression showing 3x3-th root of 5r + 23-th root of 3{x to the power of 2 {r} to the power of 3 } + 4r3-th root of {r to the power of 2 }
c A LaTex expression showing 3x3-th root of 2r + 23-th root of 2x{r to the power of 2 } + 4r3-th root of 2r
6
Add or subtract the radical expressions
A LaTex expression showing 3nsquare root of 3pn + 5psquare root of 3 + 2nsquare root of 3n
a A LaTex expression showing 3nsquare root of 3pn + 5psquare root of 3 + 2nsquare root of 3n
b A LaTex expression showing 3nsquare root of 5pn + psquare root of 5 + {n} to the power of 2 square root of 6{n to the power of 2 }
7
A LaTex expression showing 43-th root of 11{b to the power of 2 {y} to the power of 2 } - 3y3-th root of 11{b to the power of 2 y} - 2by3-th root of 11b
Add or subtract the radical expressions
a A LaTex expression showing 43-th root of 11{b to the power of 2 {y} to the power of 2 } - 3y3-th root of 11{b to the power of 2 y} - 2by3-th root of 11b
b A LaTex expression showing 3-th root of 11{b to the power of 4 y} - 5{y} to the power of 3 3-th root of 9{b to the power of 2 y} - {b} to the power of 3 {y} to the power of 3 3-th root of 10{b to the power of 3 }
c A LaTex expression showing 3-th root of 12b{y to the power of 4 } - 5{y} to the power of 2 3-th root of 14by - by3-th root of 12b