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

This math topic focuses on skills related to simplifying and performing operations with radical expressions that include both values and variables. It entails adding and subtracting radicals and requires a good understanding of combining like terms under the radical and proper handling of variable expressions within radicals. The problems are structured to encourage mastery of simplification techniques and learning how to manipulate algebraic expressions involving square roots in preparation for more advanced algebra topics.

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 275{r to the power of 4 } + square root of 99{r to the power of 2 }
a A LaTex expression showing 4{r} to the power of 3 square root of 13 + 3rsquare root of 13
b A LaTex expression showing 4{r} to the power of 2 square root of 13 + rsquare root of 7
c A LaTex expression showing 5{r} to the power of 2 square root of 11 + 3rsquare root of 11
2
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 12z - square root of 48z
a A LaTex expression showing square root of z - square root of 3{z to the power of 2 }
b A LaTex expression showing -2square root of 3{z to the power of 3 }
c A LaTex expression showing -2square root of 3{z to the power of 2 }
d A LaTex expression showing -2square root of 3z
e A LaTex expression showing square root of 3z
3
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 125{y to the power of 3 } - square root of 80y
a A LaTex expression showing 5ysquare root of 5y - 4square root of 5y
b A LaTex expression showing 3ysquare root of 3{y to the power of 3 } - 5square root of 6y
c A LaTex expression showing 8ysquare root of 5y - 6square root of y
d A LaTex expression showing 3ysquare root of 5y - square root of 4y
e A LaTex expression showing 5ysquare root of 3{y to the power of 3 } - 6square root of 5y
4
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 275c + square root of 176
a A LaTex expression showing 8square root of 12{c to the power of 3 } + 2square root of 10
b A LaTex expression showing 5square root of 11c + 4square root of 11
c A LaTex expression showing 7square root of 14{c to the power of 3 } + 4square root of 14
5
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 275y - square root of 99y
a A LaTex expression showing 2square root of y
b A LaTex expression showing 3square root of 14{y to the power of 3 } - 6square root of 8{y to the power of 3 }
c A LaTex expression showing 2square root of 11{y to the power of 3 }
d A LaTex expression showing 5square root of 10y - 6square root of 7y
e A LaTex expression showing 2square root of 11y
6
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 50 + square root of 18{x to the power of 3 }
a A LaTex expression showing 5 + 5xsquare root of x
b A LaTex expression showing 5square root of 2 + 3xsquare root of 2x
c A LaTex expression showing square root of 3 + xsquare root of x
7
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 112x + square root of 63x
a A LaTex expression showing 4square root of 3{x to the power of 2 } + 4square root of 5x
b A LaTex expression showing 7square root of 7x
c A LaTex expression showing 7square root of 7
d A LaTex expression showing 6square root of 7x + 4square root of 5x
e A LaTex expression showing 5square root of 4x + 6square root of 6x
8
Simplify, then add or subtract the radical expressions
A LaTex expression showing square root of 32{c to the power of 4 } + square root of 50c
a A LaTex expression showing 3{c} to the power of 4 square root of 5 + 3square root of c
b A LaTex expression showing 7c + 4square root of 5{c to the power of 2 }
c A LaTex expression showing 5{c} to the power of 3 + 6square root of c
d A LaTex expression showing 4{c} to the power of 2 square root of 2 + 5square root of 2c