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.

more
View

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

Mobius Math Academy logo
Radicals - Adding and Subtracting - Simplification (Values and Variables)
1
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 4dsquare root of 11d + 5rsquare root of 8 - 3dsquare root of 11
b A LaTex expression showing dsquare root of 14d + {r} to the power of 4 square root of 12 - 3dsquare root of 11
c 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
d 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
e A LaTex expression showing 4dsquare root of 11d + 2{r} to the power of 2 square root of 11 - 3dsquare root of 11
2
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 - 4rcsquare root of 2r + 4{r} to the power of 2 csquare root of 4{r to the power of 3 }
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 - 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 }
3
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 + 33-th root of 2{x to the power of 3 {m} to the power of 3 } + 3x3-th root of 3
b A LaTex expression showing 2x3-th root of 3m + 23-th root of 3xm + {x} to the power of 2
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 + 23-th root of 3xm + 3x3-th root of 3
4
A LaTex expression showing 3-th root of 320{y to the power of 3 c} - 3-th root of 320{y to the power of 4 {c} to the power of 4 } - 3-th root of 135{y to the power of 3 {c} to the power of 2 }
Simplify the radical expressions to prepare for adding or subtracting
a A LaTex expression showing 4y3-th root of 5c - 4yc3-th root of 5yc - 6y3-th root of 6{c to the power of 2 }
b A LaTex expression showing {y} to the power of 3 3-th root of 7{c to the power of 3 } - 4yc3-th root of 5yc - 3y3-th root of 5{c to the power of 2 }
c A LaTex expression showing 4y3-th root of 5c - 4yc3-th root of 5yc - 3y3-th root of 5{c to the power of 2 }
d A LaTex expression showing 7y3-th root of 8{c to the power of 2 } - 4yc3-th root of 5yc - {y} to the power of 3 3-th root of 5{c to the power of 2 }
5
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 50{b to the power of 4 {r} to the power of 3 } - square root of 50 - square root of 18{b to the power of 4 {r} to the power of 3 }
a A LaTex expression showing 2{b} to the power of 2 {r} to the power of 2 square root of r - square root of 5 - 5{b} to the power of 3 {r} to the power of 3 square root of 2r
b A LaTex expression showing 5{b} to the power of 2 rsquare root of 2r - 5square root of 2 - 3{b} to the power of 2 rsquare root of 2r
c A LaTex expression showing 5b{r} to the power of 2 square root of 3{r to the power of 3 } - 5square root of 2 - 3{b} to the power of 2 rsquare root of 2r
d A LaTex expression showing 5{b} to the power of 2 rsquare root of 2r - 3square root of 5 - 3{b} to the power of 2 rsquare root of 2r
6
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 32{m to the power of 2 {d} to the power of 2 } + square root of 8{m to the power of 2 } + square root of 32{m to the power of 3 {d} to the power of 4 }
a A LaTex expression showing {m} to the power of 3 {d} to the power of 2 square root of 2 + 2msquare root of 2 + 4m{d} to the power of 2 square root of 2m
b A LaTex expression showing 4mdsquare root of 2 + m + 3{m} to the power of 2 dsquare root of 4m
c A LaTex expression showing 4mdsquare root of 2 + 5msquare root of 4 + 4m{d} to the power of 2 square root of 2m
d A LaTex expression showing 4mdsquare root of 2 + m + 7m{d} to the power of 3 square root of m
e A LaTex expression showing 4mdsquare root of 2 + 2msquare root of 2 + 4m{d} to the power of 2 square root of 2m
7
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing 3-th root of 320{c to the power of 2 n} - 3-th root of 320c{n to the power of 4 } + 3-th root of 40c{n to the power of 2 }
a A LaTex expression showing 43-th root of 5{c to the power of 2 n} - 4n3-th root of 5cn + 23-th root of 5c{n to the power of 2 }
b A LaTex expression showing 43-th root of 5{c to the power of 2 n} - 4n3-th root of 5cn + 3-th root of 5cn
c A LaTex expression showing 43-th root of 5{c to the power of 2 n} - 7n3-th root of 6cn + 23-th root of 5c{n to the power of 2 }
d A LaTex expression showing 53-th root of 8cn - {n} to the power of 2 3-th root of 4{c to the power of 2 n} + 23-th root of 5c{n to the power of 2 }
8
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 50{y to the power of 3 {c} to the power of 4 } - square root of 8{y to the power of 4 {c} to the power of 2 } - square root of 32{y to the power of 4 {c} to the power of 4 }
a A LaTex expression showing 5y{c} to the power of 2 square root of 2y - 4{y} to the power of 4 {c} to the power of 3 - 4{y} to the power of 2 {c} to the power of 2 square root of 2
b A LaTex expression showing 5y{c} to the power of 2 square root of 2y - 2{y} to the power of 2 csquare root of 2 - 4{y} to the power of 2 {c} to the power of 2 square root of 2
c A LaTex expression showing 3y{c} to the power of 4 square root of {y to the power of 2 } - 2{y} to the power of 2 csquare root of 2 - 4{y} to the power of 2 {c} to the power of 2 square root of 2
d A LaTex expression showing 5y{c} to the power of 2 square root of 2y - 2{y} to the power of 4 {c} to the power of 2 - 4{y} to the power of 2 {c} to the power of 2 square root of 2