Adding and Subtracting from Simplified (Values and Variables) (Level 3)

This math topic focuses on adding and subtracting radical expressions involving both numerical values and variables. The problems are designed to help students practice simplifying and combining radicals that contain algebraic expressions. Some problems include expressions with different roots and powers, requiring knowledge of radical rules to add or subtract effectively. This involves manipulating expressions for addition or subtraction by ensuring the radicals have the same index and radicand, and appropriately handling coefficients and variables within the radical expressions.

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

more
View

Radicals - Adding and Subtracting from Simplified (Values and Variables) Worksheet

Mobius Math Academy logo
Radicals - Adding and Subtracting from Simplified (Values and Variables)
1
Add or subtract the radical expressions
A LaTex expression showing 3xsquare root of 11x + 4{x} to the power of 2 square root of 11
a A LaTex expression showing 3xsquare root of 11x + 4{x} to the power of 2 square root of 11
b A LaTex expression showing 6xsquare root of 14x + 4{x} to the power of 4 square root of 10
c A LaTex expression showing xsquare root of 14{x to the power of 2 } + 2xsquare root of 8
d A LaTex expression showing 3xsquare root of 12x + {x} to the power of 3 square root of 7
e A LaTex expression showing 2{x} to the power of 3 square root of 13{x to the power of 2 } + 6{x} to the power of 4 square root of 11
2
Add or subtract the radical expressions
A LaTex expression showing 2{d} to the power of 2 square root of 2 + 5square root of 2d
a A LaTex expression showing dsquare root of 3 + 7square root of 2d
b A LaTex expression showing 2d + 8square root of 5d
c A LaTex expression showing 5{d} to the power of 4 square root of 4 + 3square root of {d to the power of 2 }
d A LaTex expression showing 2{d} to the power of 2 square root of 2 + 5square root of 2d
3
Add or subtract the radical expressions
A LaTex expression showing 4square root of 3n - 2square root of 3n
a A LaTex expression showing 5square root of 3n
b A LaTex expression showing 2square root of 4n
c A LaTex expression showing 2square root of 3n - square root of 2{n to the power of 3 }
d A LaTex expression showing 2square root of 3n
e A LaTex expression showing 2square root of 3{n to the power of 3 }
4
Add or subtract the radical expressions
A LaTex expression showing 3square root of 2m + 2msquare root of 2m
a A LaTex expression showing 3square root of 5m + msquare root of 4{m to the power of 3 }
b A LaTex expression showing 4square root of 3{m to the power of 3 } + msquare root of m
c A LaTex expression showing 2square root of {m to the power of 3 } + msquare root of m
d A LaTex expression showing square root of m + 5msquare root of 2m
e A LaTex expression showing 3square root of 2m + 2msquare root of 2m
5
A LaTex expression showing 4{y} to the power of 2 square root of 11 - 3ysquare root of 11
Add or subtract the radical expressions
a A LaTex expression showing 4{y} to the power of 2 square root of 11 - 3ysquare root of 11
b A LaTex expression showing 5{y} to the power of 3 square root of 10 - {y} to the power of 3 square root of 11
6
Add or subtract the radical expressions
A LaTex expression showing 3square root of 7c + 4square root of 7c
a A LaTex expression showing 5square root of 9c + square root of 7c
b A LaTex expression showing 7square root of 7{c to the power of 3 }
c A LaTex expression showing 7square root of 7c
d A LaTex expression showing 7square root of 7{c to the power of 2 }
e A LaTex expression showing 7square root of 4c
7
Add or subtract the radical expressions
A LaTex expression showing 3square root of 5z + 4zsquare root of 5
a A LaTex expression showing 2square root of 4z + 3zsquare root of 3
b A LaTex expression showing 6square root of 6z + 3{z} to the power of 2 square root of 3
c A LaTex expression showing 3square root of 5z + 4zsquare root of 5
8
Add or subtract the radical expressions
A LaTex expression showing 4square root of 7p + 3square root of 7p
a A LaTex expression showing 7square root of 7p
b A LaTex expression showing 7square root of p
c A LaTex expression showing 4square root of 4p + 4square root of 8p
d A LaTex expression showing 7square root of 7{p to the power of 3 }
e A LaTex expression showing 5square root of 7p