Adding and Subtracting (Values and Variables) (Level 2)

This math topic focuses on adding and subtracting radicals that involve both numerical values and variables. The skills practiced involve simplifying radical expressions before performing addition or subtraction. Problems include working with different powers of variables under square roots, and combining like terms to reach a simplified result. Each question presents multiple choices for answers, challenging the learner to identify the correct simplified form of complex radical expressions. These problems help reinforce understanding of basic radical properties, manipulation for simplification, and combining radical terms effectively.

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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Radicals - Adding and Subtracting (Values and Variables)
1
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 112{x to the power of 2 } - square root of 7{x to the power of 4 }
a A LaTex expression showing 2{x} to the power of 3 square root of 7 - 2xsquare root of 10
b A LaTex expression showing xsquare root of 3 - {x} to the power of 4 square root of 7
c A LaTex expression showing 4xsquare root of 7 - {x} to the power of 2 square root of 7
d A LaTex expression showing 3xsquare root of 9 - 2{x} to the power of 4 square root of 5
2
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 11{d to the power of 2 } + square root of 44{d to the power of 4 }
a A LaTex expression showing dsquare root of 11 + 2{d} to the power of 2 square root of 11
b A LaTex expression showing 3dsquare root of 12 + 3{d} to the power of 4 square root of 10
c A LaTex expression showing {d} to the power of 2 square root of 11 + {d} to the power of 3 square root of 13
3
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 5{z to the power of 2 } - square root of 20{z to the power of 2 }
a A LaTex expression showing -1z
b A LaTex expression showing -1{z} to the power of 2 square root of 5
c A LaTex expression showing -1zsquare root of 5
d A LaTex expression showing -1square root of 5
e A LaTex expression showing zsquare root of 5
4
A LaTex expression showing square root of 112{x to the power of 4 } + square root of 7{x to the power of 2 }
Simplify, then add or subtract the radical expressions
a A LaTex expression showing 4{x} to the power of 2 square root of 7 + xsquare root of 7
b A LaTex expression showing 3xsquare root of 6 + xsquare root of 4
5
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 3{c to the power of 4 } + square root of 48
a A LaTex expression showing {c} to the power of 3 square root of 4 + 3square root of 4
b A LaTex expression showing {c} to the power of 2 square root of 3 + 4square root of 3
c A LaTex expression showing 2{c} to the power of 2 + 6square root of 2
6
A LaTex expression showing square root of 50{r to the power of 4 } - square root of 2
Simplify, then add or subtract the radical expressions
a A LaTex expression showing 6rsquare root of 3 - square root of 4
b A LaTex expression showing 5{r} to the power of 2 square root of 2 - square root of 2
7
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 18{p to the power of 3 } + square root of 2p
a A LaTex expression showing 6{p} to the power of 3 square root of p + square root of 3p
b A LaTex expression showing 5psquare root of {p to the power of 2 } + 2square root of {p to the power of 2 }
c A LaTex expression showing 3psquare root of 2p + square root of 2p
8
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 2{p to the power of 3 } - square root of 8p
a A LaTex expression showing psquare root of p - square root of 5p
b A LaTex expression showing psquare root of 2p - 2square root of 2p
c A LaTex expression showing psquare root of p - 5square root of 4p
d A LaTex expression showing psquare root of p - square root of 3p
e A LaTex expression showing {p} to the power of 3 square root of {p to the power of 2 } - 3square root of 2p