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Radicals

Adding and Subtracting - Simplification (Values and Variables) (Level 5)

This math topic focuses on skills related to radicals involving simplification of expressions with variables and constants to prepare them for addition and subtraction. These problems include various complexities such as square roots and cube roots combined with algebraic expressions involving powers and coefficients. The expressions require both understanding of radical rules and algebraic manipulation to simplify before performing operations like addition or subtraction.

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

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Radicals - Adding and Subtracting - Simplification (Values and Variables) Worksheet

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Math worksheet on 'Radicals - Adding and Subtracting - Simplification (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
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing 3-th root of 24{x to the power of 3 m} + 3-th root of 24xm + 3-th root of 81{x to the power of 3 }
a A LaTex expression showing 2x3-th root of 3m + 23-th root of 3xm + {x} to the power of 2
b A LaTex expression showing 2x3-th root of 3m + 23-th root of 3xm + 3x3-th root of 3
c A LaTex expression showing 2{x} to the power of 2 3-th root of 2m + 23-th root of 3xm + 4{x} to the power of 3 3-th root of 2
d A LaTex expression showing 2x3-th root of 3m + 33-th root of 2{x to the power of 3 {m} to the power of 3 } + 3x3-th root of 3
2
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 45{r to the power of 4 } + square root of 20{z to the power of 2 {r} to the power of 3 } + square root of 80zr
a A LaTex expression showing rsquare root of 5 + 2zrsquare root of 5r + 4square root of 5zr
b A LaTex expression showing 3{r} to the power of 2 square root of 5 + 2zrsquare root of 5r + 4square root of 5zr
c A LaTex expression showing 3{r} to the power of 2 square root of 5 + 3{z} to the power of 2 rsquare root of 6{r to the power of 3 } + 4square root of 5zr
d A LaTex expression showing 3{r} to the power of 2 square root of 5 + 2zrsquare root of 5r + 2square root of 5{z to the power of 3 {r} to the power of 3 }
3
A LaTex expression showing 3-th root of 189{m to the power of 4 {r} to the power of 2 } - 3-th root of 56m{r to the power of 3 } - 3-th root of 189{m to the power of 4 }
Simplify the radical expressions to prepare for adding or subtracting
a A LaTex expression showing 3m3-th root of 7m{r to the power of 2 } - 2r3-th root of 7m - 3m3-th root of 7m
b A LaTex expression showing 3m3-th root of 7m{r to the power of 2 } - 2r3-th root of 7m - 2m3-th root of 3m
c A LaTex expression showing 5m3-th root of 3mr - {r} to the power of 2 3-th root of 8m - 3m3-th root of 7m
d A LaTex expression showing 4{m} to the power of 3 3-th root of 8{m to the power of 3 r} - 2r3-th root of 7m - 4m3-th root of 5m
4
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 275{z to the power of 3 } + square root of 99{z to the power of 4 x} + square root of 99{z to the power of 2 }
a A LaTex expression showing 5zsquare root of 11z + 3{z} to the power of 2 square root of 11x + 2zsquare root of 14
b A LaTex expression showing 4{z} to the power of 2 square root of 14{z to the power of 3 } + 6{z} to the power of 2 square root of 8{x to the power of 3 } + 3zsquare root of 11
c A LaTex expression showing 5{z} to the power of 3 square root of 9{z to the power of 3 } + {z} to the power of 2 square root of 10{x to the power of 2 } + 3zsquare root of 11
d A LaTex expression showing 5zsquare root of 11z + 3{z} to the power of 2 square root of 11x + 3zsquare root of 11
5
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing 3-th root of 16n - 3-th root of 54{d to the power of 3 {n} to the power of 4 } + 3-th root of 54{d to the power of 3 {n} to the power of 2 }
a A LaTex expression showing 23-th root of 2n - 3dn3-th root of 2n + 3d3-th root of 2{n to the power of 2 }
b A LaTex expression showing 23-th root of 2n - 6dn3-th root of 4{n to the power of 3 } + 3{d} to the power of 2 3-th root of {n to the power of 4 }
c A LaTex expression showing 3-th root of {n to the power of 3 } - dn3-th root of 3{n to the power of 2 } + 3d3-th root of 2{n to the power of 2 }
d A LaTex expression showing 23-th root of 2n - 3dn3-th root of 2n + 3{d} to the power of 3 3-th root of n
6
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 176{d to the power of 3 } + square root of 44{r to the power of 4 } - square root of 99{d to the power of 2 }
a A LaTex expression showing 3dsquare root of 10{d to the power of 3 } + 2{r} to the power of 2 square root of 11 - 6dsquare root of 9
b A LaTex expression showing 4dsquare root of 11d + 5rsquare root of 8 - 3dsquare root of 11
c A LaTex expression showing dsquare root of 14d + {r} to the power of 4 square root of 12 - 3dsquare root of 11
d A LaTex expression showing 5{d} to the power of 3 square root of 10d + 2{r} to the power of 2 square root of 11 - 3dsquare root of 11
e A LaTex expression showing 4dsquare root of 11d + 2{r} to the power of 2 square root of 11 - 3dsquare root of 11
7
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 50{r to the power of 3 {c} to the power of 4 } - square root of 32{r to the power of 3 {c} to the power of 2 } + square root of 32{r to the power of 3 {c} to the power of 4 }
a A LaTex expression showing 5r{c} to the power of 2 square root of 2r - 4rcsquare root of 2r + 4r{c} to the power of 2 square root of 2r
b A LaTex expression showing 5r{c} to the power of 2 square root of 2r - 2{r} to the power of 2 {c} to the power of 2 square root of {r to the power of 3 } + 2rcsquare root of {r to the power of 2 }
c A LaTex expression showing 5r{c} to the power of 2 square root of 2r - 4rcsquare root of 2r + 3{r} to the power of 2 csquare root of 3{r to the power of 3 }
d A LaTex expression showing 5r{c} to the power of 2 square root of 2r - 4rcsquare root of 2r + 4{r} to the power of 2 csquare root of 4{r to the power of 3 }