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Radicals - Adding and Subtracting - Simplification (Values and Variables) (Level 4)

This math topic focuses on the addition and subtraction of radical expressions, specifically emphasizing their simplification involving both numerical values and variables. Students engage in combining like terms and simplifying under the radical, requiring a good understanding of exponent rules, multiplication, and division within the context of radicals. The topic forms a part of an introduction to more advanced algebraic techniques dealing with radical expressions. The questions include both square roots and higher-order roots, and covers scenarios including different powers and coefficients to challenge and improve algebraic manipulation skills related to 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

50c3r4+18c4r4+18c3r3\sqrt{50{c}^{3}{r}^{4}} + \sqrt{18{c}^{4}{r}^{4}} + \sqrt{18{c}^{3}{r}^{3}}

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 4)'. 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 56y - 3-th root of 189{y to the power of 4 {p} to the power of 2 } + 3-th root of 56yp
a A LaTex expression showing 23-th root of 7y - 3y3-th root of 7y{p to the power of 2 } + 3-th root of 8yp
b A LaTex expression showing 43-th root of 7y - 3y3-th root of 7y{p to the power of 2 } + 3-th root of 4y{p to the power of 3 }
c A LaTex expression showing 23-th root of 7y - 3y3-th root of 7y{p to the power of 2 } + 23-th root of 7yp
d A LaTex expression showing 23-th root of 7y - 2y3-th root of 5{y to the power of 2 {p} to the power of 4 } + 43-th root of 3y{p to the power of 2 }
e A LaTex expression showing 23-th root of 7y - y3-th root of 5{y to the power of 3 {p} to the power of 4 } + 23-th root of 7yp
f A LaTex expression showing 23-th root of 7y - 5y3-th root of 10yp + 23-th root of 7yp
2
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 44{c to the power of 2 {r} to the power of 2 } + square root of 99{r to the power of 2 } + square root of 44{c to the power of 4 {r} to the power of 3 }
a A LaTex expression showing 2crsquare root of 11 + 2rsquare root of 9 + 2{c} to the power of 2 rsquare root of 11r
b A LaTex expression showing 2crsquare root of 11 + 3rsquare root of 11 + 3crsquare root of 7r
c A LaTex expression showing 4crsquare root of 8 + {r} to the power of 3 square root of 13 + 2{c} to the power of 2 rsquare root of 11r
d A LaTex expression showing 3crsquare root of 9 + 3rsquare root of 11 + 2{c} to the power of 2 rsquare root of 11r
e A LaTex expression showing 2crsquare root of 11 + 3rsquare root of 11 + 2{c} to the power of 2 rsquare root of 11r
f A LaTex expression showing 2crsquare root of 11 + 3rsquare root of 11 + {c} to the power of 2 rsquare root of 14{r to the power of 2 }
3
A LaTex expression showing square root of 45{c to the power of 2 m} - square root of 45{c to the power of 3 {m} to the power of 4 } - square root of 20{c to the power of 3 {m} to the power of 4 }
Simplify the radical expressions to prepare for adding or subtracting
a A LaTex expression showing 3csquare root of 5m - 3c{m} to the power of 2 square root of 5c - 3{c} to the power of 3 {m} to the power of 4 square root of c
b A LaTex expression showing 3csquare root of 5m - 3c{m} to the power of 2 square root of 5c - c{m} to the power of 2 square root of 2c
c A LaTex expression showing 3csquare root of 5m - 3c{m} to the power of 2 square root of 5c - 2cmsquare root of 6{c to the power of 2 }
d A LaTex expression showing 3csquare root of 5m - 3c{m} to the power of 2 square root of 5c - 3c{m} to the power of 3 square root of 7{c to the power of 3 }
e A LaTex expression showing 3csquare root of 5m - 3c{m} to the power of 2 square root of 5c - 2c{m} to the power of 2 square root of 5c
f A LaTex expression showing 3csquare root of 5m - 3c{m} to the power of 2 square root of 5c - {c} to the power of 2 msquare root of 5{c to the power of 2 }
4
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 27cn - square root of 27{c to the power of 2 {n} to the power of 3 } + square root of 48{c to the power of 3 {n} to the power of 3 }
a A LaTex expression showing 3square root of 3cn - 3cnsquare root of 3n + 4cnsquare root of 3cn
b A LaTex expression showing 3square root of 3c{n to the power of 2 } - cnsquare root of {n to the power of 3 } + 4cnsquare root of 3cn
c A LaTex expression showing 3square root of 3cn - 3cnsquare root of 3n + 3{c} to the power of 2 nsquare root of {c to the power of 2 n}
d A LaTex expression showing 4square root of cn - 3cnsquare root of 3n + 3cnsquare root of 6cn
e A LaTex expression showing square root of 3c{n to the power of 3 } - 3cnsquare root of 3n + 4{c} to the power of 2 {n} to the power of 2 square root of 3{c to the power of 2 n}
f A LaTex expression showing square root of cn - 2cnsquare root of {n to the power of 2 } + 4cnsquare root of 3cn
5
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing 3-th root of 88{n to the power of 4 {b} to the power of 4 } + 3-th root of 88{n to the power of 2 {b} to the power of 4 } - 3-th root of 297{n to the power of 2 b}
a A LaTex expression showing 2nb3-th root of 11nb + 2b3-th root of 11{n to the power of 2 b} - 3-th root of 9{n to the power of 2 b}
b A LaTex expression showing 3{n} to the power of 2 {b} to the power of 3 3-th root of 13nb + 2b3-th root of 11{n to the power of 2 b} - 33-th root of 11{n to the power of 2 b}
c A LaTex expression showing 2nb3-th root of 11nb + 2b3-th root of 11{n to the power of 2 b} - 33-th root of 11{n to the power of 2 b}
d A LaTex expression showing n{b} to the power of 2 3-th root of 10{n to the power of 3 b} + 2b3-th root of 11{n to the power of 2 b} - 3-th root of 9nb
e A LaTex expression showing n{b} to the power of 2 3-th root of 10nb + b3-th root of 12n{b to the power of 2 } - 43-th root of 7{n to the power of 2 {b} to the power of 3 }
f A LaTex expression showing 2nb3-th root of 11nb + 2b3-th root of 11{n to the power of 2 b} - 23-th root of 10{n to the power of 2 {b} to the power of 3 }
6
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing 3-th root of 24{n to the power of 4 p} - 3-th root of 81{n to the power of 4 {p} to the power of 3 } - 3-th root of 24{n to the power of 4 {p} to the power of 3 }
a A LaTex expression showing 2n3-th root of 3np - 6{n} to the power of 3 p3-th root of 6n - 2np3-th root of 3n
b A LaTex expression showing 2n3-th root of 5{n to the power of 2 {p} to the power of 2 } - 3np3-th root of 3n - 2np3-th root of 3n
c A LaTex expression showing 4{n} to the power of 3 3-th root of 5np - 3np3-th root of 3n - 2np3-th root of 3n
d A LaTex expression showing 2n3-th root of 3np - 6n{p} to the power of 2 3-th root of {n to the power of 2 } - 4np3-th root of 4n
e A LaTex expression showing 5{n} to the power of 3 3-th root of {n to the power of 2 p} - 3np3-th root of 3n - 5np3-th root of n
f A LaTex expression showing 2n3-th root of 3np - 3np3-th root of 3n - 2np3-th root of 3n
7
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 48{b to the power of 4 } - square root of 48n{b to the power of 2 } - square root of 75n{b to the power of 2 }
a A LaTex expression showing 4{b} to the power of 2 square root of 3 - 6bsquare root of 5n - 5bsquare root of 3n
b A LaTex expression showing 4{b} to the power of 2 square root of 3 - bsquare root of 5{n to the power of 2 } - 5bsquare root of 3n
c A LaTex expression showing 4{b} to the power of 2 square root of 3 - 4bsquare root of 3n - 5bsquare root of 3n
d A LaTex expression showing 2b - 4bsquare root of 3n - 5bsquare root of 3n
e A LaTex expression showing 7b - 4bsquare root of 3n - 2bsquare root of n
f A LaTex expression showing bsquare root of 4 - 4bsquare root of 3n - 5bsquare root of 3n