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

This math topic focuses on simplifying radical expressions involving both values and variables to prepare for addition and subtraction. It includes step-by-step problems that require learners to work with square roots of numerical coefficients and variable terms. The expressions often involve combining like terms or simplifying expressions under radical signs before performing addition or subtraction. Each question presents various scenarios and possible simplifications, reflecting how to handle radicals in basic algebraic operations effectively.

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

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

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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 5{b to the power of 2 } - square root of 45
a A LaTex expression showing bsquare root of 5 - 3square root of 5
b A LaTex expression showing bsquare root of 5 - 2
c A LaTex expression showing bsquare root of 5 - square root of 4
2
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 2{y to the power of 3 } + square root of 50{y to the power of 4 }
a A LaTex expression showing ysquare root of 2y + 3{y} to the power of 2 square root of 2
b A LaTex expression showing ysquare root of 2y + {y} to the power of 4 square root of 4
c A LaTex expression showing ysquare root of 2y + 5{y} to the power of 2 square root of 2
d A LaTex expression showing ysquare root of 2y + {y} to the power of 3
3
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 12{p to the power of 2 } - square root of 3
a A LaTex expression showing 5psquare root of 2 - square root of 3
b A LaTex expression showing 4psquare root of 6 - 3square root of 2
c A LaTex expression showing 2psquare root of 3 - square root of 3
4
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 7 - square root of 175{x to the power of 3 }
a A LaTex expression showing square root of 10 - 5xsquare root of 7x
b A LaTex expression showing square root of 7 - 5xsquare root of 7x
c A LaTex expression showing 2square root of 5 - 5xsquare root of 7x
d A LaTex expression showing 2square root of 6 - 5xsquare root of 7x
5
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 7{p to the power of 3 } + square root of 28{p to the power of 2 }
a A LaTex expression showing {p} to the power of 2 square root of 10p + 2psquare root of 7
b A LaTex expression showing psquare root of 7p + {p} to the power of 3 square root of 5
c A LaTex expression showing psquare root of 7p + 2psquare root of 7
d A LaTex expression showing 3{p} to the power of 2 square root of 5p + 2psquare root of 7
e A LaTex expression showing psquare root of 7p + {p} to the power of 3 square root of 9
6
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 18{c to the power of 3 } - square root of 2
a A LaTex expression showing 4csquare root of 2{c to the power of 3 } - square root of 2
b A LaTex expression showing 2csquare root of {c to the power of 3 } - square root of 2
c A LaTex expression showing 3csquare root of 2c - square root of 2
d A LaTex expression showing csquare root of 3{c to the power of 2 } - square root of 2
7
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 2{r to the power of 4 } + square root of 32{r to the power of 4 }
a A LaTex expression showing rsquare root of 5 + 4{r} to the power of 2 square root of 2
b A LaTex expression showing {r} to the power of 2 square root of 2 + 4{r} to the power of 2 square root of 2
c A LaTex expression showing {r} to the power of 2 square root of 2 + 2{r} to the power of 2
d A LaTex expression showing rsquare root of 4 + 3{r} to the power of 4 square root of 5
8
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 3z + square root of 75{z to the power of 4 }
a A LaTex expression showing square root of 3z + 5{z} to the power of 2 square root of 3
b A LaTex expression showing square root of 3z + 5{z} to the power of 4
c A LaTex expression showing square root of 3z + 3{z} to the power of 2
d A LaTex expression showing square root of 3z + 7{z} to the power of 2