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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Square - Simplifying, Values and Variables, Radical Remaining

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Simplify the radical

45by5\sqrt{45b{y}^{5}}

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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 8{m to the power of 4 {b} to the power of 2 }
a A LaTex expression showing {m} to the power of 4 {b} to the power of 2
b A LaTex expression showing 4mb
c A LaTex expression showing m{b} to the power of 3 square root of 2
d A LaTex expression showing 2{m} to the power of 2 bsquare root of 2
e A LaTex expression showing {m} to the power of 2 b
f A LaTex expression showing mb
2
Simplify the radical
A LaTex expression showing square root of 48{d to the power of 5 r}
a A LaTex expression showing dsquare root of d{r to the power of 3 }
b A LaTex expression showing 6{d} to the power of 2 square root of 3dr
c A LaTex expression showing 2dsquare root of dr
d A LaTex expression showing 5{d} to the power of 3 square root of 2dr
e A LaTex expression showing 6{d} to the power of 2 square root of {d to the power of 3 r}
f A LaTex expression showing 4{d} to the power of 2 square root of 3dr
3
Simplify the radical
A LaTex expression showing square root of 112{x to the power of 3 {b} to the power of 5 }
a A LaTex expression showing 4x{b} to the power of 2 square root of 7xb
b A LaTex expression showing 6x{b} to the power of 3 square root of 6{x to the power of 3 {b} to the power of 2 }
c A LaTex expression showing 5xbsquare root of 4x{b to the power of 2 }
d A LaTex expression showing 6{x} to the power of 3 bsquare root of 7xb
e A LaTex expression showing 6{x} to the power of 2 bsquare root of 5xb
f A LaTex expression showing 7x{b} to the power of 2 square root of 8xb
4
Simplify the radical
A LaTex expression showing square root of 27n{b to the power of 3 }
a A LaTex expression showing 3bsquare root of n{b to the power of 2 }
b A LaTex expression showing 5bsquare root of 6nb
c A LaTex expression showing 3bsquare root of 3nb
d A LaTex expression showing 2{b} to the power of 3 square root of 2{n to the power of 3 {b} to the power of 2 }
e A LaTex expression showing bsquare root of {n to the power of 3 b}
f A LaTex expression showing bsquare root of {n to the power of 3 {b} to the power of 2 }
5
Simplify the radical
A LaTex expression showing square root of 50{c to the power of 4 {r} to the power of 4 }
a A LaTex expression showing 3c{r} to the power of 4 square root of 4
b A LaTex expression showing 4crsquare root of 5
c A LaTex expression showing 2c{r} to the power of 4 square root of 3
d A LaTex expression showing 4{c} to the power of 2 {r} to the power of 4 square root of 2
e A LaTex expression showing 5{c} to the power of 2 {r} to the power of 2 square root of 2
f A LaTex expression showing 4c{r} to the power of 4 square root of 4
6
Simplify the radical
A LaTex expression showing square root of 99{r to the power of 3 c}
a A LaTex expression showing {r} to the power of 3 square root of 13{r to the power of 3 c}
b A LaTex expression showing 2{r} to the power of 2 square root of 11rc
c A LaTex expression showing rsquare root of 7r{c to the power of 3 }
d A LaTex expression showing 3rsquare root of 11rc
e A LaTex expression showing rsquare root of 11{r to the power of 2 {c} to the power of 2 }
f A LaTex expression showing rsquare root of 7{r to the power of 2 c}
7
Simplify the radical
A LaTex expression showing square root of 27{d to the power of 5 {z} to the power of 3 }
a A LaTex expression showing 3d{z} to the power of 3 square root of {d to the power of 2 {z} to the power of 2 }
b A LaTex expression showing 4{d} to the power of 3 {z} to the power of 2 square root of {d to the power of 2 {z} to the power of 2 }
c A LaTex expression showing 3{d} to the power of 2 zsquare root of 3dz
d A LaTex expression showing 4{d} to the power of 3 zsquare root of {d to the power of 3 z}
e A LaTex expression showing 3{d} to the power of 3 {z} to the power of 2 square root of {d to the power of 2 {z} to the power of 3 }
f A LaTex expression showing {d} to the power of 2 zsquare root of 3d{z to the power of 2 }