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

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Simplify the radical expressions to prepare for adding or subtracting

5z2−45z\sqrt{5{z}^{2}} - \sqrt{45z}

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 45{n to the power of 3 } + square root of 5{n to the power of 2 }
a A LaTex expression showing 3nsquare root of 5n + nsquare root of 8
b A LaTex expression showing 3nsquare root of 5n + 2nsquare root of 6
c A LaTex expression showing 6nsquare root of 8{n to the power of 3 } + nsquare root of 7
d A LaTex expression showing 5nsquare root of n + 4nsquare root of 2
e A LaTex expression showing 3nsquare root of 5n + nsquare root of 5
f A LaTex expression showing 3nsquare root of 5n + n
2
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 3p + square root of 75{p to the power of 4 }
a A LaTex expression showing square root of 3p + 5{p} to the power of 2 square root of 3
b A LaTex expression showing 3square root of p + 5{p} to the power of 2 square root of 3
c A LaTex expression showing square root of 3p + 4{p} to the power of 3 square root of 5
d A LaTex expression showing 4square root of 3{p to the power of 3 } + 6{p} to the power of 4 square root of 4
e A LaTex expression showing square root of 3p + 5psquare root of 3
f A LaTex expression showing square root of 3p + 5{p} to the power of 3 square root of 3
3
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 44{x to the power of 3 } + square root of 11x
a A LaTex expression showing {x} to the power of 3 square root of 11x + square root of 11x
b A LaTex expression showing 2xsquare root of 11x + 4square root of 14x
c A LaTex expression showing 2xsquare root of 11x + square root of 11x
d A LaTex expression showing xsquare root of 7x + square root of 11x
e A LaTex expression showing 5xsquare root of 13x + square root of 11x
f A LaTex expression showing 2xsquare root of 11x + 2square root of 10{x to the power of 3 }
4
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 3{b to the power of 2 } + square root of 75{b to the power of 3 }
a A LaTex expression showing b + 5bsquare root of 3b
b A LaTex expression showing bsquare root of 3 + 5bsquare root of 3b
c A LaTex expression showing 4{b} to the power of 3 + 8bsquare root of 4b
d A LaTex expression showing bsquare root of 3 + 4bsquare root of {b to the power of 3 }
e A LaTex expression showing 2bsquare root of 3 + 5bsquare root of 3b
f A LaTex expression showing 2bsquare root of 3 + 3bsquare root of b
5
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 63{r to the power of 3 } + square root of 7r
a A LaTex expression showing 3rsquare root of 7r + square root of 7r
b A LaTex expression showing 3rsquare root of 7r + square root of 8{r to the power of 2 }
c A LaTex expression showing 4rsquare root of 8r + square root of 7r
d A LaTex expression showing 3rsquare root of 7r + 4square root of 9{r to the power of 3 }
e A LaTex expression showing 3rsquare root of 7r + 2square root of 7{r to the power of 3 }
f A LaTex expression showing 5{r} to the power of 3 square root of 3r + square root of 6{r to the power of 3 }
6
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 32{y to the power of 4 } - square root of 2y
a A LaTex expression showing 4{y} to the power of 2 square root of 2 - square root of 3y
b A LaTex expression showing 4{y} to the power of 2 square root of 2 - square root of y
c A LaTex expression showing 3{y} to the power of 4 square root of 3 - 2square root of {y to the power of 2 }
d A LaTex expression showing 4{y} to the power of 2 square root of 2 - square root of 2{y to the power of 3 }
e A LaTex expression showing 4{y} to the power of 2 square root of 2 - square root of 2y
f A LaTex expression showing 3{y} to the power of 3 square root of 3 - square root of 2y
7
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 80{c to the power of 2 } - square root of 5
a A LaTex expression showing 4csquare root of 5 - square root of 4
b A LaTex expression showing 4csquare root of 5 - square root of 5
c A LaTex expression showing 4csquare root of 5 - 1
d A LaTex expression showing csquare root of 2 - square root of 5
e A LaTex expression showing 4csquare root of 5 - square root of 3
f A LaTex expression showing 4csquare root of 7 - 1