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Radicals - 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

20m5y2\sqrt{20{m}^{5}{y}^{2}}

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 125m{y to the power of 3 }
a A LaTex expression showing 5ysquare root of 5my
b A LaTex expression showing ysquare root of 6my
c A LaTex expression showing 4ysquare root of 5m{y to the power of 2 }
d A LaTex expression showing 6ysquare root of 2{m to the power of 2 y}
e A LaTex expression showing 4{y} to the power of 3 square root of 3my
f A LaTex expression showing 5{y} to the power of 3 square root of 8m{y to the power of 3 }
2
Simplify the radical
A LaTex expression showing square root of 32{b to the power of 5 {n} to the power of 2 }
a A LaTex expression showing 4{b} to the power of 2 nsquare root of 2b
b A LaTex expression showing 4{b} to the power of 3 nsquare root of b
c A LaTex expression showing {b} to the power of 3 {n} to the power of 3 square root of {b to the power of 2 }
d A LaTex expression showing 6bnsquare root of 2{b to the power of 3 }
e A LaTex expression showing 4bnsquare root of b
f A LaTex expression showing 6b{n} to the power of 2 square root of b
3
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 5{c} to the power of 2 {r} to the power of 2 square root of 2
b A LaTex expression showing 3c{r} to the power of 4 square root of 4
c A LaTex expression showing 4c{r} to the power of 4 square root of 4
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 2c{r} to the power of 4 square root of 3
f A LaTex expression showing 4crsquare root of 5
4
Simplify the radical
A LaTex expression showing square root of 20{p to the power of 2 {m} to the power of 2 }
a A LaTex expression showing 5p{m} to the power of 2
b A LaTex expression showing p{m} to the power of 2 square root of 2
c A LaTex expression showing pm
d A LaTex expression showing pmsquare root of 5
e A LaTex expression showing pmsquare root of 2
f A LaTex expression showing 2pmsquare root of 5
5
Simplify the radical
A LaTex expression showing square root of 63{y to the power of 2 p}
a A LaTex expression showing {y} to the power of 3 square root of 7p
b A LaTex expression showing 2{y} to the power of 3 square root of 3p
c A LaTex expression showing 5{y} to the power of 3 square root of 9{p to the power of 2 }
d A LaTex expression showing 3ysquare root of 7p
e A LaTex expression showing {y} to the power of 2 square root of 7p
f A LaTex expression showing 4ysquare root of 3{p to the power of 3 }
6
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 6{x} to the power of 3 bsquare root of 7xb
b A LaTex expression showing 4x{b} to the power of 2 square root of 7xb
c A LaTex expression showing 7x{b} to the power of 2 square root of 8xb
d 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 }
e A LaTex expression showing 6{x} to the power of 2 bsquare root of 5xb
f A LaTex expression showing 5xbsquare root of 4x{b to the power of 2 }
7
Simplify the radical
A LaTex expression showing square root of 175{z to the power of 3 {d} to the power of 5 }
a A LaTex expression showing {z} to the power of 3 {d} to the power of 4 square root of 9z{d to the power of 2 }
b A LaTex expression showing 2z{d} to the power of 2 square root of 4z{d to the power of 2 }
c A LaTex expression showing 5{z} to the power of 3 {d} to the power of 2 square root of 5zd
d A LaTex expression showing 8zdsquare root of 5{z to the power of 2 {d} to the power of 2 }
e A LaTex expression showing 5z{d} to the power of 2 square root of 7zd
f A LaTex expression showing 3z{d} to the power of 2 square root of 5zd