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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

44c2r2+99r2+44c4r3\sqrt{44{c}^{2}{r}^{2}} + \sqrt{99{r}^{2}} + \sqrt{44{c}^{4}{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 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 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 }
b 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}
c 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}
d 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}
e 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
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 }
2
A LaTex expression showing square root of 125{d to the power of 3 {n} to the power of 3 } + square root of 20{d to the power of 3 {n} to the power of 4 } + square root of 80{d to the power of 3 n}
Simplify the radical expressions to prepare for adding or subtracting
a A LaTex expression showing 5dnsquare root of 5dn + 2d{n} to the power of 2 square root of 5d + 3dsquare root of {d to the power of 2 n}
b A LaTex expression showing 5dnsquare root of 5dn + {d} to the power of 2 {n} to the power of 2 square root of 2d + 4dsquare root of 5dn
c A LaTex expression showing 5dnsquare root of 5dn + 2d{n} to the power of 2 square root of 5d + 4dsquare root of 5dn
d A LaTex expression showing 3{d} to the power of 3 {n} to the power of 2 square root of 2{d to the power of 2 {n} to the power of 3 } + {d} to the power of 3 {n} to the power of 4 square root of 5d + 4dsquare root of 5dn
e A LaTex expression showing 7{d} to the power of 3 {n} to the power of 3 square root of 3dn + 4{d} to the power of 2 nsquare root of 2{d to the power of 2 } + 4dsquare root of 5dn
f A LaTex expression showing 5dnsquare root of 5dn + 2d{n} to the power of 2 square root of 5d + 6dsquare root of 3dn
3
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing 3-th root of 128{z to the power of 3 {n} to the power of 4 } - 3-th root of 16{z to the power of 3 {n} to the power of 3 } + 3-th root of 54{z to the power of 3 }
a A LaTex expression showing 4zn3-th root of 2n - 2z{n} to the power of 3 3-th root of 3 + 6z
b A LaTex expression showing 4zn3-th root of 2n - 2zn3-th root of 2 + 6z3-th root of 4
c A LaTex expression showing 7z{n} to the power of 2 3-th root of 2{n to the power of 2 } - zn + 3z3-th root of 2
d A LaTex expression showing 4zn3-th root of 2n - 2z{n} to the power of 2 3-th root of 5 + 3z3-th root of 2
e A LaTex expression showing 6{z} to the power of 2 n3-th root of 3{n to the power of 3 } - 4z{n} to the power of 2 + 5{z} to the power of 2 3-th root of 3
f A LaTex expression showing 4zn3-th root of 2n - 2zn3-th root of 2 + 3z3-th root of 2
4
A LaTex expression showing square root of 176{c to the power of 2 {x} to the power of 2 } - square root of 176{c to the power of 2 {x} to the power of 3 } + square root of 275{c to the power of 3 {x} to the power of 2 }
Simplify the radical expressions to prepare for adding or subtracting
a A LaTex expression showing 4cxsquare root of 11 - 4cxsquare root of 11x + 5cxsquare root of 11c
b A LaTex expression showing cxsquare root of 11 - 6cxsquare root of 7{x to the power of 2 } + 5cxsquare root of 11c
c A LaTex expression showing 4cxsquare root of 11 - 7c{x} to the power of 2 square root of 7x + 5cxsquare root of 11c
d A LaTex expression showing 4cxsquare root of 11 - {c} to the power of 3 xsquare root of 10{x to the power of 2 } + 7cxsquare root of 14c
e A LaTex expression showing cxsquare root of 14 - 4cxsquare root of 11x + 8c{x} to the power of 3 square root of 7{c to the power of 3 }
f A LaTex expression showing 4cxsquare root of 11 - 4cxsquare root of 11x + 2cxsquare root of 7c
5
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 + 3rsquare root of 11 + {c} to the power of 2 rsquare root of 14{r to the power of 2 }
b A LaTex expression showing 2crsquare root of 11 + 2rsquare root of 9 + 2{c} to the power of 2 rsquare root of 11r
c A LaTex expression showing 2crsquare root of 11 + 3rsquare root of 11 + 2{c} to the power of 2 rsquare root of 11r
d 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
e A LaTex expression showing 3crsquare root of 9 + 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 + 3crsquare root of 7r
6
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing 3-th root of 54 - 3-th root of 128{d to the power of 4 r} - 3-th root of 54{d to the power of 3 {r} to the power of 4 }
a A LaTex expression showing 33-th root of 2 - 7d3-th root of d{r to the power of 3 } - 3dr3-th root of 2r
b A LaTex expression showing 6 - 4d3-th root of 2dr - 3dr3-th root of 2r
c A LaTex expression showing 33-th root of 2 - 7d3-th root of {d to the power of 3 r} - dr3-th root of 2{r to the power of 3 }
d A LaTex expression showing 23-th root of 2 - d3-th root of dr - 3dr3-th root of 2r
e A LaTex expression showing 33-th root of 2 - 4d3-th root of 2dr - 3dr3-th root of 2r
f A LaTex expression showing 3-th root of 3 - 4{d} to the power of 2 3-th root of {d to the power of 3 {r} to the power of 3 } - {d} to the power of 3 {r} to the power of 2 3-th root of {r to the power of 2 }
7
Simplify the radical expressions to prepare for adding or subtracting
A LaTex expression showing square root of 176{y to the power of 2 } - square root of 99{y to the power of 4 } - square root of 275{m to the power of 3 {y} to the power of 3 }
a A LaTex expression showing 4ysquare root of 7 - 3{y} to the power of 2 square root of 11 - 5mysquare root of 11my
b A LaTex expression showing 4ysquare root of 11 - 3{y} to the power of 2 square root of 11 - 5mysquare root of 14my
c A LaTex expression showing 4ysquare root of 11 - 3{y} to the power of 2 square root of 11 - 5mysquare root of 11my
d A LaTex expression showing 4ysquare root of 11 - 4ysquare root of 13 - 5mysquare root of 11my
e A LaTex expression showing 7ysquare root of 7 - 3{y} to the power of 2 square root of 11 - 5mysquare root of 11my
f A LaTex expression showing 6{y} to the power of 2 square root of 12 - 3{y} to the power of 2 square root of 11 - 8mysquare root of 8my