Radicals - Square - Simplifying, Values and Variables, Radical Remaining (Level 2)

This math topic involves practicing techniques for simplifying radical expressions, specifically square roots involving variables and coefficients. The problems include various complexities by incorporating different powers of variables within the radicands. Skills tested include factoring under the radical and handling variables within radicals, maintaining a balance between coefficients and radicand components post-simplification. The questions encourage mastery in extracting squares from under radicals and simplifying the expressions effectively to their simplest forms. This involves recognizing perfect squares and properly manipulating the powers of variables.

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

80m3\sqrt{80{m}^{3}}

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 2)'. Part of a broader unit on 'Radicals - Simplifying Practice' Learn online: app.mobius.academy/math/units/radicals_simplifying_practice/
1
Simplify the radical
A LaTex expression showing square root of 20z
a A LaTex expression showing 4square root of 7{z to the power of 3 }
b A LaTex expression showing 4square root of 8z
c A LaTex expression showing 3square root of 3{z to the power of 2 }
d A LaTex expression showing 2square root of 5z
e A LaTex expression showing square root of 5{z to the power of 3 }
f A LaTex expression showing square root of 3z
2
Simplify the radical
A LaTex expression showing square root of 99{c to the power of 3 }
a A LaTex expression showing 3{c} to the power of 3 square root of 12c
b A LaTex expression showing 6{c} to the power of 3 square root of 7{c to the power of 3 }
c A LaTex expression showing 3csquare root of 14c
d A LaTex expression showing 6{c} to the power of 3 square root of 14c
e A LaTex expression showing 3csquare root of 11c
f A LaTex expression showing 6csquare root of 8c
3
Simplify the radical
A LaTex expression showing square root of 176{x to the power of 3 }
a A LaTex expression showing 7{x} to the power of 3 square root of 9x
b A LaTex expression showing xsquare root of 7x
c A LaTex expression showing 5xsquare root of 7x
d A LaTex expression showing 4xsquare root of 11x
e A LaTex expression showing xsquare root of 13x
f A LaTex expression showing {x} to the power of 2 square root of 11{x to the power of 3 }
4
Simplify the radical
A LaTex expression showing square root of 63y
a A LaTex expression showing 5square root of 3{y to the power of 3 }
b A LaTex expression showing 3square root of 7y
c A LaTex expression showing 4square root of 6y
d A LaTex expression showing 3square root of 8y
e A LaTex expression showing 2square root of 4y
f A LaTex expression showing 4square root of 10{y to the power of 2 }
5
Simplify the radical
A LaTex expression showing square root of 27{d to the power of 2 }
a A LaTex expression showing {d} to the power of 3
b A LaTex expression showing 3dsquare root of 3
c A LaTex expression showing 4dsquare root of 6
d A LaTex expression showing {d} to the power of 2
e A LaTex expression showing dsquare root of 2
f A LaTex expression showing 3dsquare root of 6
6
Simplify the radical
A LaTex expression showing square root of 32{x to the power of 4 }
a A LaTex expression showing 4{x} to the power of 2 square root of 2
b A LaTex expression showing 6{x} to the power of 2 square root of 5
c A LaTex expression showing 6x
d A LaTex expression showing 6{x} to the power of 3
e A LaTex expression showing 4{x} to the power of 3 square root of 4
f A LaTex expression showing {x} to the power of 4
7
Simplify the radical
A LaTex expression showing square root of 112{b to the power of 3 }
a A LaTex expression showing bsquare root of 7{b to the power of 2 }
b A LaTex expression showing 7{b} to the power of 2 square root of 6b
c A LaTex expression showing 4bsquare root of 7b
d A LaTex expression showing 4{b} to the power of 2 square root of 6b
e A LaTex expression showing bsquare root of 8b
f A LaTex expression showing 4bsquare root of 3b