Square - Simplifying, Values and Variables, Radical Remaining (Level 3)

This math topic focuses on advanced techniques for simplifying square roots involving radicals, particularly when dealing with algebraic expressions that include variables and coefficients. The problems require extracting perfect squares from under the radical and simplifying the remaining expressions. Each question presents a radical expression and multiple choice answers, challenging students to apply their skills in algebraic manipulation and understanding of radical properties to find the simplest form. The problems target an understanding of how to handle higher powers and coefficients within square roots effectively.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Radicals - Square - Simplifying, Values and Variables, Radical Remaining Worksheet

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Math worksheet on 'Radicals - Square - Simplifying, Values and Variables, Radical Remaining (Level 3)'. Part of a broader unit on 'Radicals - Simplifying Advanced' Learn online: app.mobius.academy/math/units/radicals_simplifying_advanced/
1
Simplify the radical
A LaTex expression showing square root of 275{n to the power of 2 {m} to the power of 2 }
a A LaTex expression showing 3{n} to the power of 3 {m} to the power of 3 square root of 9
b A LaTex expression showing 7nmsquare root of 10
c A LaTex expression showing 5nmsquare root of 11
d A LaTex expression showing nmsquare root of 11
e A LaTex expression showing 4n{m} to the power of 3 square root of 11
2
Simplify the radical
A LaTex expression showing square root of 20{x to the power of 5 {d} to the power of 4 }
a A LaTex expression showing 2{x} to the power of 2 {d} to the power of 2 square root of 5x
b A LaTex expression showing {x} to the power of 4 dsquare root of 7{x to the power of 2 }
c A LaTex expression showing {x} to the power of 4 {d} to the power of 2 square root of 2{x to the power of 3 }
d A LaTex expression showing x{d} to the power of 3 square root of 3x
e A LaTex expression showing 3x{d} to the power of 3 square root of 6x
3
Simplify the radical
A LaTex expression showing square root of 125{p to the power of 5 {c} to the power of 5 }
a A LaTex expression showing 6pcsquare root of 7{p to the power of 3 {c} to the power of 3 }
b A LaTex expression showing {p} to the power of 4 {c} to the power of 3 square root of 5{p to the power of 2 c}
c A LaTex expression showing 3pcsquare root of 2p{c to the power of 3 }
d A LaTex expression showing 2{p} to the power of 3 {c} to the power of 2 square root of 3{p to the power of 2 c}
e A LaTex expression showing 5{p} to the power of 2 {c} to the power of 2 square root of 5pc
4
Simplify the radical
A LaTex expression showing square root of 99{z to the power of 3 {m} to the power of 5 }
a A LaTex expression showing zmsquare root of 13{z to the power of 2 {m} to the power of 2 }
b A LaTex expression showing 6z{m} to the power of 4 square root of 12{z to the power of 2 {m} to the power of 3 }
c A LaTex expression showing {z} to the power of 3 {m} to the power of 4 square root of 7{z to the power of 2 {m} to the power of 3 }
d A LaTex expression showing 5z{m} to the power of 2 square root of 9{z to the power of 3 {m} to the power of 2 }
e A LaTex expression showing 3z{m} to the power of 2 square root of 11zm
5
Simplify the radical
A LaTex expression showing square root of 63{r to the power of 4 {m} to the power of 2 }
a A LaTex expression showing 3{r} to the power of 2 msquare root of 7
b A LaTex expression showing 3{r} to the power of 2 msquare root of 3
c A LaTex expression showing 3{r} to the power of 4 {m} to the power of 2 square root of 4
d A LaTex expression showing 2{r} to the power of 4 {m} to the power of 2 square root of 8
e A LaTex expression showing 4r{m} to the power of 3 square root of 9
6
Simplify the radical
A LaTex expression showing square root of 32{r to the power of 5 {d} to the power of 5 }
a A LaTex expression showing 4{r} to the power of 2 {d} to the power of 2 square root of rd
b A LaTex expression showing 4{r} to the power of 3 dsquare root of {r to the power of 2 {d} to the power of 2 }
c A LaTex expression showing 4{r} to the power of 4 dsquare root of {r to the power of 3 d}
d A LaTex expression showing {r} to the power of 2 {d} to the power of 3 square root of 4rd
e A LaTex expression showing 4{r} to the power of 2 {d} to the power of 2 square root of 2rd
7
Simplify the radical
A LaTex expression showing square root of 45b{y to the power of 5 }
a A LaTex expression showing 3{y} to the power of 2 square root of 2{b to the power of 3 y}
b A LaTex expression showing 3{y} to the power of 2 square root of 5by
c A LaTex expression showing 4{y} to the power of 2 square root of 3{b to the power of 3 y}
d A LaTex expression showing 3{y} to the power of 4 square root of 8{b to the power of 2 y}
e A LaTex expression showing ysquare root of 8b{y to the power of 3 }