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Radicals - Adding and Subtracting - Simplification (Values and Variables) (Level 3)

This math topic focuses on simplifying radical expressions involving various powers and roots, such as square roots combined with integer and variable terms. The challenges specifically involve adding and subtracting these radical expressions after simplification. Each question presents a radical equation with multiple outcomes for students to determine the correct simplified form. The material is designed to enhance understanding of manipulating and combining radicals, tailored for students with prior knowledge, as indicated by the inclusion of values and variables within the radicals.

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

45b+80\sqrt{45b} + \sqrt{80}

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 3)'. 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 75 + square root of 27{c to the power of 2 }
a A LaTex expression showing 5square root of 3 + 2c
b A LaTex expression showing 8 + 2csquare root of 5
c A LaTex expression showing 8square root of 6 + 3csquare root of 3
d A LaTex expression showing 3square root of 4 + 4{c} to the power of 2 square root of 6
e A LaTex expression showing 4square root of 3 + 5c
f A LaTex expression showing 5square root of 3 + 3csquare root of 3
2
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 125{n to the power of 2 } + square root of 45n
a A LaTex expression showing 5nsquare root of 5 + square root of {n to the power of 2 }
b A LaTex expression showing 5nsquare root of 5 + 3square root of 4n
c A LaTex expression showing 7{n} to the power of 3 square root of 3 + 3square root of 5n
d A LaTex expression showing 5nsquare root of 5 + square root of 7n
e A LaTex expression showing 5nsquare root of 5 + 4square root of 6n
f A LaTex expression showing 5nsquare root of 5 + 3square root of 5n
3
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 176{b to the power of 2 } + square root of 99
a A LaTex expression showing 3bsquare root of 8 + 6square root of 9
b A LaTex expression showing 2{b} to the power of 3 square root of 9 + 3square root of 11
c A LaTex expression showing 4bsquare root of 11 + 3square root of 11
d A LaTex expression showing 4bsquare root of 11 + square root of 9
e A LaTex expression showing 7{b} to the power of 2 square root of 7 + 3square root of 11
f A LaTex expression showing {b} to the power of 3 square root of 14 + 5square root of 11
4
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 12{c to the power of 3 } + square root of 75
a A LaTex expression showing {c} to the power of 3 square root of {c to the power of 3 } + 5square root of 3
b A LaTex expression showing csquare root of 3{c to the power of 3 } + 5square root of 3
c A LaTex expression showing 2csquare root of 3c + 6
d A LaTex expression showing 2csquare root of 3c + 4
e A LaTex expression showing 5csquare root of 2c + 5square root of 3
f A LaTex expression showing 2csquare root of 3c + 5square root of 3
5
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 50{c to the power of 4 } + square root of 18{c to the power of 3 }
a A LaTex expression showing 5{c} to the power of 2 square root of 2 + csquare root of {c to the power of 2 }
b A LaTex expression showing 5{c} to the power of 2 square root of 2 + csquare root of 5{c to the power of 3 }
c A LaTex expression showing 5{c} to the power of 2 square root of 2 + 6{c} to the power of 3 square root of 4{c to the power of 2 }
d A LaTex expression showing 4{c} to the power of 3 + 2csquare root of c
e A LaTex expression showing 5{c} to the power of 2 square root of 2 + 5{c} to the power of 2 square root of c
f A LaTex expression showing 5{c} to the power of 2 square root of 2 + 3csquare root of 2c
6
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 8{c to the power of 3 } - square root of 50c
a A LaTex expression showing 2csquare root of 2c - 6square root of {c to the power of 3 }
b A LaTex expression showing 2csquare root of 2c - 8square root of 2c
c A LaTex expression showing 5{c} to the power of 3 square root of 4{c to the power of 3 } - 5square root of 2c
d A LaTex expression showing 2csquare root of 2c - 4square root of c
e A LaTex expression showing 2csquare root of 2c - 5square root of 2c
f A LaTex expression showing {c} to the power of 3 square root of c - square root of 3c
7
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 48{d to the power of 3 } - square root of 27{d to the power of 4 }
a A LaTex expression showing 4dsquare root of 3d - 3{d} to the power of 2 square root of 3
b A LaTex expression showing 6dsquare root of 6d - 3{d} to the power of 2 square root of 3
c A LaTex expression showing {d} to the power of 3 square root of d - 3{d} to the power of 2 square root of 3
d A LaTex expression showing 5dsquare root of 6d - 3{d} to the power of 2 square root of 3
e A LaTex expression showing 5dsquare root of 3{d to the power of 3 } - 2{d} to the power of 4 square root of 6
f A LaTex expression showing 5{d} to the power of 3 square root of d - 3{d} to the power of 2 square root of 3