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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

12−27\sqrt{12} - \sqrt{27}

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 48 - square root of 75
a A LaTex expression showing 4square root of 3 - 7square root of 2
b A LaTex expression showing 4square root of 3 - 5square root of 3
c A LaTex expression showing 2square root of 2 - 5square root of 3
d A LaTex expression showing 4square root of 3 - 3
e A LaTex expression showing square root of 3 - 5square root of 3
f A LaTex expression showing 5 - 5square root of 3
2
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 - 8square root of 2c
b A LaTex expression showing {c} to the power of 3 square root of c - square root of 3c
c A LaTex expression showing 2csquare root of 2c - 4square root of c
d A LaTex expression showing 2csquare root of 2c - 5square root of 2c
e 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
f A LaTex expression showing 2csquare root of 2c - 6square root of {c to the power of 3 }
3
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 32{n to the power of 4 } + square root of 18{n to the power of 3 }
a A LaTex expression showing 4{n} to the power of 2 square root of 2 + {n} to the power of 3 square root of 3n
b A LaTex expression showing {n} to the power of 3 square root of 3 + 3{n} to the power of 3 square root of n
c A LaTex expression showing 3{n} to the power of 3 + 4nsquare root of 4n
d A LaTex expression showing 4{n} to the power of 2 square root of 2 + 3nsquare root of 2n
e A LaTex expression showing 4{n} to the power of 2 square root of 2 + nsquare root of n
f A LaTex expression showing 4{n} to the power of 2 square root of 2 + nsquare root of 2n
4
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 5{c to the power of 3 }
b 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 }
c A LaTex expression showing 5{c} to the power of 2 square root of 2 + csquare root of {c to the power of 2 }
d A LaTex expression showing 5{c} to the power of 2 square root of 2 + 3csquare root of 2c
e A LaTex expression showing 4{c} to the power of 3 + 2csquare root of c
f 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
5
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 176{m to the power of 4 } + square root of 99m
a A LaTex expression showing 7{m} to the power of 4 square root of 12 + 3square root of 11m
b A LaTex expression showing {m} to the power of 2 square root of 12 + 3square root of 11m
c A LaTex expression showing 4{m} to the power of 2 square root of 11 + 3square root of 11m
d A LaTex expression showing 4{m} to the power of 2 square root of 11 + 6square root of 11{m to the power of 2 }
e A LaTex expression showing 7msquare root of 11 + 3square root of 11m
f A LaTex expression showing 4{m} to the power of 4 square root of 11 + 3square root of 11m
6
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 63{z to the power of 4 } + square root of 112{z to the power of 2 }
a A LaTex expression showing 3{z} to the power of 2 square root of 7 + 5zsquare root of 4
b A LaTex expression showing 3{z} to the power of 2 square root of 7 + 6zsquare root of 4
c A LaTex expression showing 5zsquare root of 10 + 4zsquare root of 7
d A LaTex expression showing 3{z} to the power of 2 square root of 7 + 5{z} to the power of 3 square root of 7
e A LaTex expression showing 3{z} to the power of 2 square root of 7 + 4zsquare root of 7
f A LaTex expression showing 3{z} to the power of 3 square root of 8 + 4zsquare root of 7
7
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 12y + square root of 48
a A LaTex expression showing 2square root of 3y + 4square root of 3
b A LaTex expression showing 2square root of 3y + 5square root of 4
c A LaTex expression showing square root of 4y + 4square root of 3
d A LaTex expression showing 2square root of 3y + 1
e A LaTex expression showing square root of 3y + 6square root of 6
f A LaTex expression showing 2square root of 3y + 7square root of 6