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

This math topic focuses on the addition and subtraction of radical expressions, specifically emphasizing their simplification involving both numerical values and variables. Students engage in combining like terms and simplifying under the radical, requiring a good understanding of exponent rules, multiplication, and division within the context of radicals. The topic forms a part of an introduction to more advanced algebraic techniques dealing with radical expressions. The questions include both square roots and higher-order roots, and covers scenarios including different powers and coefficients to challenge and improve algebraic manipulation skills related to radicals.

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 3-th root of 135{c to the power of 3 {d} to the power of 2 } - 3-th root of 40{c to the power of 3 {d} to the power of 2 } - 3-th root of 135
a A LaTex expression showing 3c3-th root of 5{d to the power of 2 } - 2c3-th root of 5{d to the power of 2 } - 33-th root of 5
b A LaTex expression showing c3-th root of 2{d to the power of 3 } - 3{c} to the power of 3 3-th root of 8d - 33-th root of 5
c A LaTex expression showing 3c3-th root of 5{d to the power of 2 } - 2c3-th root of 5{d to the power of 2 } - 33-th root of 6
d A LaTex expression showing 3c3-th root of 5{d to the power of 2 } - 3c3-th root of 4{d to the power of 4 } - 33-th root of 5
2
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing 3-th root of 81{p to the power of 2 d} + 3-th root of 24{p to the power of 4 } + 3-th root of 81{p to the power of 2 {d} to the power of 2 }
a A LaTex expression showing 33-th root of 3{p to the power of 2 d} + {p} to the power of 3 3-th root of 4p + 33-th root of 3{p to the power of 2 {d} to the power of 2 }
b A LaTex expression showing 33-th root of 3{p to the power of 2 d} + 2p3-th root of 3p + 33-th root of 3{p to the power of 2 {d} to the power of 2 }
c A LaTex expression showing 3-th root of {p to the power of 4 {d} to the power of 3 } + 3{p} to the power of 3 3-th root of 4{p to the power of 3 } + 33-th root of 3{p to the power of 2 {d} to the power of 2 }
d A LaTex expression showing 33-th root of 3{p to the power of 2 d} + 2p3-th root of 3p + 3-th root of 3p{d to the power of 4 }
3
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 12{b to the power of 2 {z} to the power of 4 } + square root of 48{b to the power of 4 {z} to the power of 3 } - square root of 75{z to the power of 2 }
a A LaTex expression showing 2b{z} to the power of 2 square root of 3 + 6{b} to the power of 4 zsquare root of 4z - 5zsquare root of 3
b A LaTex expression showing 2b{z} to the power of 2 square root of 3 + 4{b} to the power of 2 zsquare root of 3z - 7zsquare root of 3
c A LaTex expression showing 2b{z} to the power of 2 square root of 3 + 4{b} to the power of 2 zsquare root of 3z - 5zsquare root of 3
d A LaTex expression showing 2b{z} to the power of 2 square root of 3 + 4{b} to the power of 2 zsquare root of 3z - 8{z} to the power of 2 square root of 3
e A LaTex expression showing b{z} to the power of 2 + 4{b} to the power of 2 zsquare root of 3z - 5zsquare root of 3
4
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing 3-th root of 16{p to the power of 4 {m} to the power of 3 } + 3-th root of 54p{m to the power of 4 } - 3-th root of 16
a A LaTex expression showing 2pm3-th root of 2p + 4{m} to the power of 3 3-th root of 4pm - 23-th root of 2
b A LaTex expression showing 2pm3-th root of 2p + 3m3-th root of 2pm - 23-th root of 2
c A LaTex expression showing 3p{m} to the power of 3 3-th root of 3p + 3m3-th root of 2pm - 23-th root of 2
d A LaTex expression showing 2pm3-th root of 5{p to the power of 3 } + 3m3-th root of 2pm - 1
e A LaTex expression showing 2pm3-th root of 2p + 3m3-th root of 2pm - 1
5
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 99{r to the power of 4 {b} to the power of 3 } + square root of 99b - square root of 176r
a A LaTex expression showing 3{r} to the power of 2 bsquare root of 11b + 3square root of 11b - square root of 10r
b A LaTex expression showing {r} to the power of 2 bsquare root of 8b + 3square root of 11b - 3square root of 10{r to the power of 3 }
c A LaTex expression showing 3{r} to the power of 2 bsquare root of 11b + 4square root of 12b - 6square root of 13r
d A LaTex expression showing 3{r} to the power of 2 bsquare root of 11b + 3square root of 11b - 4square root of 12r
e A LaTex expression showing 3{r} to the power of 2 bsquare root of 11b + 3square root of 11b - 4square root of 11r
6
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing 3-th root of 81 + 3-th root of 24{p to the power of 2 {b} to the power of 2 } - 3-th root of 24{b to the power of 2 }
a A LaTex expression showing 6 + 23-th root of 3{p to the power of 2 {b} to the power of 2 } - 23-th root of 3{b to the power of 2 }
b A LaTex expression showing 2 + 23-th root of 3{p to the power of 2 {b} to the power of 2 } - 23-th root of 3{b to the power of 2 }
c A LaTex expression showing 33-th root of 3 + 23-th root of 3{p to the power of 2 {b} to the power of 2 } - 23-th root of 3{b to the power of 2 }
7
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing 3-th root of 128 + 3-th root of 54y - 3-th root of 16{b to the power of 3 y}
a A LaTex expression showing 3-th root of 5 + 33-th root of 2y - 2b3-th root of 2y
b A LaTex expression showing 43-th root of 2 + 33-th root of 2y - 5b3-th root of 2y
c A LaTex expression showing 43-th root of 2 + 53-th root of 2{y to the power of 2 } - {b} to the power of 3 3-th root of 2y
d A LaTex expression showing 43-th root of 2 + 33-th root of 2y - 2b3-th root of 2y
8
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 80y{z to the power of 3 } - square root of 45{y to the power of 4 z} + square root of 45{y to the power of 2 {z} to the power of 3 }
a A LaTex expression showing 4zsquare root of 5yz - ysquare root of 6z + 3yzsquare root of 5z
b A LaTex expression showing 4zsquare root of 5yz - {y} to the power of 3 square root of 2{z to the power of 3 } + 3yzsquare root of 5z
c A LaTex expression showing 4zsquare root of 5yz - 3{y} to the power of 2 square root of 5z + 3yzsquare root of 5z
d A LaTex expression showing 4zsquare root of 5yz - 5{y} to the power of 4 square root of 3{z to the power of 2 } + 3yzsquare root of 5z
e A LaTex expression showing 4zsquare root of 5yz - 2ysquare root of 7z + 3yzsquare root of 5z