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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Math worksheet on 'Radicals - Adding and Subtracting - Simplification (Values and Variables) (Level 2)'. Part of a broader unit on 'Radicals - Addition and Subtraction Intro' Learn online: app.mobius.academy/math/units/radicals_addition_and_subtraction_intro/
1
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 6 - 5xsquare root of 7x
d A LaTex expression showing 2square root of 5 - 5xsquare root of 7x
2
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 5{y to the power of 3 } + square root of 45{y to the power of 4 }
a A LaTex expression showing ysquare root of 5y + 3{y} to the power of 2 square root of 5
b A LaTex expression showing {y} to the power of 2 square root of 4y + 3{y} to the power of 2 square root of 5
c A LaTex expression showing ysquare root of 7{y to the power of 2 } + 2ysquare root of 5
d A LaTex expression showing ysquare root of 5y + ysquare root of 3
3
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 3csquare root of 2c - 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 4csquare root of 2{c to the power of 3 } - square root of 2
d A LaTex expression showing csquare root of 3{c to the power of 2 } - square root of 2
4
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 7{c to the power of 4 } - square root of 112{c to the power of 3 }
a A LaTex expression showing {c} to the power of 2 square root of 7 - 4csquare root of 7c
b A LaTex expression showing {c} to the power of 2 square root of 7 - {c} to the power of 2 square root of 5c
c A LaTex expression showing csquare root of 9 - 4csquare root of 7c
d A LaTex expression showing {c} to the power of 2 square root of 7 - 3csquare root of 6c
5
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 176{r to the power of 4 } + square root of 11r
a A LaTex expression showing 4{r} to the power of 2 square root of 11 + square root of 11r
b A LaTex expression showing 4{r} to the power of 2 square root of 11 + square root of 7r
c A LaTex expression showing 2{r} to the power of 3 square root of 11 + square root of 11r
6
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 18z + square root of 2
a A LaTex expression showing 3square root of 2z + 1
b A LaTex expression showing 4square root of 4z + square root of 2
c A LaTex expression showing 3square root of 2z + square root of 5
d A LaTex expression showing 3square root of 2z + square root of 2
7
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 7{n to the power of 4 } + square root of 175{n to the power of 3 }
a A LaTex expression showing nsquare root of 5 + 3nsquare root of 9n
b A LaTex expression showing 4nsquare root of 3 + 5nsquare root of 7n
c A LaTex expression showing {n} to the power of 2 square root of 7 + 5{n} to the power of 2 square root of 7n
d A LaTex expression showing {n} to the power of 3 square root of 8 + nsquare root of 9n
e A LaTex expression showing {n} to the power of 2 square root of 7 + 5nsquare root of 7n