Adding and Subtracting (Values and Variables) (Level 4)

This math topic focuses on the practice of adding and subtracting radicals, specifically covering both radicals involving numerical values and those with variables. Each of the seven questions requires the student to simplify radical expressions, then perform addition or subtraction. The radical expressions vary across different indices and include mixed variables, testing a student's ability to manipulate and simplify under root terms systematically. This is part of introductory learning to radical addition and subtraction.

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

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Radicals - Adding and Subtracting (Values and Variables) Worksheet

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Math worksheet on 'Radicals - Adding and Subtracting (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
Simplify, then add or subtract the radical expressions
A LaTex expression showing 3-th root of 128c{p to the power of 4 } + 3-th root of 16{c to the power of 4 p} + 3-th root of 16{c to the power of 2 {p} to the power of 2 }
a A LaTex expression showing 5{p} to the power of 3 3-th root of 2{c to the power of 3 {p} to the power of 2 } + 3{c} to the power of 2 3-th root of c{p to the power of 3 } + 33-th root of 2c{p to the power of 4 }
b A LaTex expression showing {p} to the power of 2 3-th root of 5{c to the power of 2 p} + 5c3-th root of 2cp + 3-th root of c{p to the power of 4 }
c A LaTex expression showing 4p3-th root of 2cp + 2c3-th root of 2cp + 23-th root of 2{c to the power of 2 {p} to the power of 2 }
2
A LaTex expression showing 3-th root of 88{y to the power of 4 } - 3-th root of 297{y to the power of 3 {x} to the power of 2 } + 3-th root of 297{y to the power of 3 {x} to the power of 4 }
Simplify, then add or subtract the radical expressions
a A LaTex expression showing y3-th root of 9y - {y} to the power of 3 3-th root of 8x + 6yx3-th root of 13x
b A LaTex expression showing 2y3-th root of 11y - 3y3-th root of 11{x to the power of 2 } + 3yx3-th root of 11x
c A LaTex expression showing 5y3-th root of 7y - 6{y} to the power of 2 3-th root of 7{x to the power of 3 } + {y} to the power of 2 {x} to the power of 2 3-th root of 12{x to the power of 2 }
3
Simplify, then add or subtract the radical expressions
A LaTex expression showing 3-th root of 128{y to the power of 4 } + 3-th root of 128{x to the power of 4 } + 3-th root of 54{x to the power of 2 y}
a A LaTex expression showing 7{y} to the power of 3 3-th root of y + 3{x} to the power of 3 3-th root of 2{x to the power of 3 } + 3-th root of 4{x to the power of 2 y}
b A LaTex expression showing 4y3-th root of 2y + 4x3-th root of 2x + 33-th root of 2{x to the power of 2 y}
c A LaTex expression showing 4{y} to the power of 3 3-th root of 3y + 3x3-th root of x + 3-th root of 5x{y to the power of 3 }
4
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 80{r to the power of 3 {x} to the power of 2 } - square root of 20r{x to the power of 2 } - square root of 125{r to the power of 2 x}
a A LaTex expression showing 2rxsquare root of 4{r to the power of 2 } - 3{x} to the power of 3 square root of {r to the power of 2 } - 3rsquare root of 2{x to the power of 3 }
b A LaTex expression showing 4rxsquare root of 5r - 2xsquare root of 5r - 5rsquare root of 5x
c A LaTex expression showing 6{r} to the power of 2 {x} to the power of 2 square root of 6r - 2xsquare root of 6{r to the power of 2 } - 3{r} to the power of 2 square root of 4{x to the power of 3 }
5
Simplify, then add or subtract the radical expressions
A LaTex expression showing 3-th root of 320{n to the power of 3 {y} to the power of 3 } - 3-th root of 320{n to the power of 4 } - 3-th root of 135{n to the power of 3 }
a A LaTex expression showing n{y} to the power of 2 3-th root of 4 - 5n3-th root of 8{n to the power of 2 } - 4{n} to the power of 3 3-th root of 7
b A LaTex expression showing ny - 2{n} to the power of 2 3-th root of 4{n to the power of 3 } - 6n3-th root of 2
c A LaTex expression showing 4ny3-th root of 5 - 4n3-th root of 5n - 3n3-th root of 5
6
Simplify, then add or subtract the radical expressions
A LaTex expression showing 3-th root of 704b{x to the power of 3 } + 3-th root of 88{b to the power of 2 {x} to the power of 3 } - 3-th root of 88{x to the power of 2 }
a A LaTex expression showing 4x3-th root of 7{b to the power of 3 } + 4{x} to the power of 3 3-th root of 13{b to the power of 3 } - 53-th root of 13{x to the power of 4 }
b A LaTex expression showing 4x3-th root of 11b + 2x3-th root of 11{b to the power of 2 } - 23-th root of 11{x to the power of 2 }
7
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 32x{c to the power of 4 } - square root of 18{x to the power of 4 {c} to the power of 4 } + square root of 50{c to the power of 4 }
a A LaTex expression showing 6{c} to the power of 3 square root of {x to the power of 2 } - {x} to the power of 2 {c} to the power of 3 + 5c
b A LaTex expression showing 4{c} to the power of 2 square root of 2x - 3{x} to the power of 2 {c} to the power of 2 square root of 2 + 5{c} to the power of 2 square root of 2
c A LaTex expression showing 7{c} to the power of 3 square root of {x to the power of 3 } - 4x{c} to the power of 4 square root of 3 + 4csquare root of 3
d A LaTex expression showing 3csquare root of 4{x to the power of 3 } - x{c} to the power of 2 + 5c