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Radicals - Adding and Subtracting - Simplification (Values and Variables) (Level 5)

This math topic focuses on skills related to radicals involving simplification of expressions with variables and constants to prepare them for addition and subtraction. These problems include various complexities such as square roots and cube roots combined with algebraic expressions involving powers and coefficients. The expressions require both understanding of radical rules and algebraic manipulation to simplify before performing operations like addition or subtraction.

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

189y3x33−56y33−189y2x3\sqrt[3]{189{y}^{3}{x}^{3}} - \sqrt[3]{56{y}^{3}} - \sqrt[3]{189{y}^{2}x}

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 5)'. 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 3-th root of 88{n to the power of 3 r} + 3-th root of 88n{r to the power of 2 } + 3-th root of 297n{r to the power of 2 }
a A LaTex expression showing 2n3-th root of 11r + 23-th root of 13n{r to the power of 3 } + 33-th root of 11n{r to the power of 2 }
b A LaTex expression showing n3-th root of 9r + 53-th root of 11n{r to the power of 3 } + 33-th root of 11n{r to the power of 2 }
c A LaTex expression showing n3-th root of 9r + 23-th root of 11n{r to the power of 2 } + 33-th root of 11n{r to the power of 2 }
d A LaTex expression showing 2{n} to the power of 2 3-th root of 12r + 23-th root of 11n{r to the power of 2 } + 33-th root of 11n{r to the power of 2 }
e A LaTex expression showing 2n3-th root of 14{r to the power of 2 } + 23-th root of 11n{r to the power of 2 } + 33-th root of 11n{r to the power of 2 }
f A LaTex expression showing 2n3-th root of 11r + 23-th root of 11n{r to the power of 2 } + 33-th root of 11n{r to the power of 2 }
2
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing 3-th root of 704z{y to the power of 3 } + 3-th root of 704y + 3-th root of 88z{y to the power of 2 }
a A LaTex expression showing 4y3-th root of 11z + 63-th root of 10y + 23-th root of 11z{y to the power of 2 }
b A LaTex expression showing 4y3-th root of 11z + 43-th root of 11y + 33-th root of 14zy
c A LaTex expression showing 4y3-th root of 11z + 3-th root of 12y + 23-th root of 11z{y to the power of 2 }
d A LaTex expression showing 4y3-th root of 11z + 43-th root of 11y + 3-th root of 14z{y to the power of 4 }
e A LaTex expression showing 4y3-th root of 11z + 43-th root of 11y + 23-th root of 11z{y to the power of 2 }
f A LaTex expression showing 4y3-th root of 11z + 73-th root of 11y + 53-th root of 13{z to the power of 2 y}
3
A LaTex expression showing square root of 28{x to the power of 3 {d} to the power of 4 } + square root of 112{x to the power of 2 {d} to the power of 2 } + square root of 175x{d to the power of 3 }
Simplify the radical expressions to prepare for adding or subtracting
a A LaTex expression showing 4x{d} to the power of 3 square root of 7{x to the power of 3 } + 4xdsquare root of 7 + 5dsquare root of 7xd
b A LaTex expression showing x{d} to the power of 4 square root of 9x + {x} to the power of 3 dsquare root of 10 + 5dsquare root of 7xd
c A LaTex expression showing 2x{d} to the power of 2 square root of 7x + 4xdsquare root of 7 + 7{d} to the power of 2 square root of 5{x to the power of 3 {d} to the power of 2 }
d A LaTex expression showing 2x{d} to the power of 2 square root of 7x + 4xdsquare root of 7 + 5dsquare root of 7xd
e A LaTex expression showing 2x{d} to the power of 2 square root of 7x + 4xdsquare root of 7 + 6{d} to the power of 2 square root of 7xd
f A LaTex expression showing 4xdsquare root of 10x + 4xdsquare root of 7 + 4dsquare root of 9{x to the power of 3 d}
4
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 28{b to the power of 3 {n} to the power of 4 } + square root of 63{b to the power of 4 {n} to the power of 3 } + square root of 175n
a A LaTex expression showing 5{b} to the power of 3 {n} to the power of 3 square root of 4b + 3{b} to the power of 2 nsquare root of 7n + 5square root of 7n
b A LaTex expression showing 2b{n} to the power of 2 square root of 7b + 2{b} to the power of 4 {n} to the power of 3 square root of 3n + 5square root of 7n
c A LaTex expression showing 2b{n} to the power of 2 square root of 7b + 3{b} to the power of 2 nsquare root of 7n + 4square root of 6n
d A LaTex expression showing 2b{n} to the power of 2 square root of 7b + 3{b} to the power of 2 nsquare root of 7n + 5square root of 5n
e A LaTex expression showing 2b{n} to the power of 2 square root of 7b + b{n} to the power of 2 square root of 8n + 5square root of 7n
f A LaTex expression showing 2b{n} to the power of 2 square root of 7b + 3{b} to the power of 2 nsquare root of 7n + 5square root of 7n
5
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 50 - square root of 32{y to the power of 4 {z} to the power of 4 } - square root of 32{y to the power of 2 }
a A LaTex expression showing 5square root of 2 - yzsquare root of 3 - 4ysquare root of 2
b A LaTex expression showing 5square root of 5 - 4{y} to the power of 2 {z} to the power of 2 square root of 2 - 4{y} to the power of 2
c A LaTex expression showing 3square root of 2 - 4{y} to the power of 2 {z} to the power of 2 square root of 2 - 4ysquare root of 2
d A LaTex expression showing 5square root of 2 - 7yz - 4ysquare root of 2
e A LaTex expression showing 5square root of 2 - 4{y} to the power of 2 {z} to the power of 2 square root of 2 - {y} to the power of 2
f A LaTex expression showing 5square root of 2 - 4{y} to the power of 2 {z} to the power of 2 square root of 2 - 4ysquare root of 2
6
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing 3-th root of 88{z to the power of 2 x} + 3-th root of 704x + 3-th root of 88{x to the power of 2 }
a A LaTex expression showing 33-th root of 13{z to the power of 2 x} + 43-th root of 11x + 23-th root of 11{x to the power of 2 }
b A LaTex expression showing 3-th root of 9{z to the power of 2 x} + 43-th root of 11x + 23-th root of 11{x to the power of 2 }
c A LaTex expression showing 23-th root of 11{z to the power of 2 x} + 3-th root of 9x + 23-th root of 11{x to the power of 2 }
d A LaTex expression showing 3-th root of 14{z to the power of 3 {x} to the power of 3 } + 3-th root of 9{x to the power of 2 } + 23-th root of 11{x to the power of 2 }
e A LaTex expression showing 23-th root of 11{z to the power of 2 x} + 43-th root of 11x + 23-th root of 11{x to the power of 2 }
f A LaTex expression showing 53-th root of 13z{x to the power of 2 } + 43-th root of 11x + 23-th root of 11{x to the power of 2 }
7
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing 3-th root of 88{d to the power of 3 {r} to the power of 2 } - 3-th root of 297{d to the power of 3 {r} to the power of 4 } + 3-th root of 704{d to the power of 4 }
a A LaTex expression showing 2d3-th root of 11{r to the power of 2 } - 3dr3-th root of 11r + 4d3-th root of 11d
b A LaTex expression showing 2d3-th root of 11{r to the power of 2 } - 2d{r} to the power of 3 3-th root of 11r + 5d3-th root of 7{d to the power of 2 }
c A LaTex expression showing 2d3-th root of 11{r to the power of 2 } - 5d{r} to the power of 2 3-th root of 9r + 4d3-th root of 11d
d A LaTex expression showing 3d3-th root of 9{r to the power of 2 } - 3dr3-th root of 11r + 4d3-th root of 11d
e A LaTex expression showing {d} to the power of 3 3-th root of 10{r to the power of 4 } - 4dr3-th root of 7{r to the power of 3 } + 7d3-th root of 12d
f A LaTex expression showing {d} to the power of 2 3-th root of 12r - {d} to the power of 3 r3-th root of 9r + 4{d} to the power of 3 3-th root of 10{d to the power of 2 }