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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

20n2+5n2\sqrt{20{n}^{2}} + \sqrt{5{n}^{2}}

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 27d - square root of 3{d to the power of 3 }
a A LaTex expression showing 3square root of 3d - dsquare root of 3d
b A LaTex expression showing 3square root of 3d - 2dsquare root of 2d
c A LaTex expression showing square root of 2d - dsquare root of 3d
d A LaTex expression showing 4square root of 3{d to the power of 2 } - dsquare root of 3d
e A LaTex expression showing 3square root of 3d - dsquare root of 2d
f A LaTex expression showing 5square root of 6d - 3{d} to the power of 2 square root of 3{d to the power of 2 }
2
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 12y - square root of 3{y to the power of 4 }
a A LaTex expression showing 2square root of 3y - {y} to the power of 3 square root of 4
b A LaTex expression showing 2square root of 3y - {y} to the power of 4 square root of 2
c A LaTex expression showing 2square root of 3y - 4{y} to the power of 2 square root of 2
d A LaTex expression showing 2square root of 3y - {y} to the power of 4
e A LaTex expression showing square root of 2y - {y} to the power of 2 square root of 3
f A LaTex expression showing 2square root of 3y - {y} to the power of 2 square root of 3
3
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 99{z to the power of 3 } + square root of 11{z to the power of 4 }
a A LaTex expression showing 3zsquare root of 11z + {z} to the power of 4 square root of 13
b A LaTex expression showing 3zsquare root of 11z + 2{z} to the power of 3 square root of 7
c A LaTex expression showing 3zsquare root of 11z + {z} to the power of 2 square root of 11
d A LaTex expression showing 2{z} to the power of 2 square root of 13z + {z} to the power of 2 square root of 11
e A LaTex expression showing zsquare root of 9z + zsquare root of 8
f A LaTex expression showing 3zsquare root of 11z + zsquare root of 12
4
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 18{d to the power of 4 } + square root of 2{d to the power of 2 }
a A LaTex expression showing 3{d} to the power of 2 square root of 2 + d
b A LaTex expression showing 3{d} to the power of 4 + dsquare root of 2
c A LaTex expression showing 3{d} to the power of 2 square root of 2 + dsquare root of 2
d A LaTex expression showing 3{d} to the power of 2 square root of 2 + 4{d} to the power of 2 square root of 4
e A LaTex expression showing 4{d} to the power of 4 square root of 4 + 3d
f A LaTex expression showing 3{d} to the power of 2 square root of 2 + 3dsquare root of 2
5
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 11p + square root of 176p
a A LaTex expression showing square root of 10p + 4square root of 11p
b A LaTex expression showing square root of 11p + 6square root of 13{p to the power of 2 }
c A LaTex expression showing square root of 11p + 4square root of 11p
d A LaTex expression showing 2square root of 7p + square root of 7{p to the power of 3 }
e A LaTex expression showing square root of 11p + square root of 9p
f A LaTex expression showing square root of 13{p to the power of 3 } + 4square root of 11p
6
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 6nsquare root of 8{n to the power of 3 } + nsquare root of 7
c A LaTex expression showing 5nsquare root of n + 4nsquare root of 2
d A LaTex expression showing 3nsquare root of 5n + n
e A LaTex expression showing 3nsquare root of 5n + nsquare root of 5
f A LaTex expression showing 3nsquare root of 5n + 2nsquare root of 6
7
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 175{d to the power of 3 } - square root of 7
a A LaTex expression showing 6dsquare root of 6d - square root of 7
b A LaTex expression showing 5dsquare root of 7d - 3square root of 5
c A LaTex expression showing {d} to the power of 3 square root of 5{d to the power of 3 } - square root of 10
d A LaTex expression showing {d} to the power of 2 square root of 6d - square root of 7
e A LaTex expression showing 5dsquare root of 7d - square root of 7
f A LaTex expression showing 5{d} to the power of 3 square root of 7d - square root of 7