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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

18y\sqrt{18y}

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 Intro' Learn online: app.mobius.academy/math/units/radicals_simplifying_intro/
1
Simplify the radical
A LaTex expression showing square root of 45{b to the power of 3 }
a A LaTex expression showing bsquare root of 3b
b A LaTex expression showing {b} to the power of 3 square root of 7b
c A LaTex expression showing 5{b} to the power of 2 square root of 3{b to the power of 3 }
d A LaTex expression showing 6bsquare root of 6{b to the power of 2 }
e A LaTex expression showing 2{b} to the power of 3 square root of 2b
f A LaTex expression showing 3bsquare root of 5b
2
Simplify the radical
A LaTex expression showing square root of 125{r to the power of 3 }
a A LaTex expression showing 5{r} to the power of 2 square root of 2{r to the power of 3 }
b A LaTex expression showing 6rsquare root of 5{r to the power of 3 }
c A LaTex expression showing rsquare root of 8{r to the power of 2 }
d A LaTex expression showing 7{r} to the power of 2 square root of 4{r to the power of 3 }
e A LaTex expression showing 5rsquare root of 5r
f A LaTex expression showing 7{r} to the power of 3 square root of 2{r to the power of 2 }
3
Simplify the radical
A LaTex expression showing square root of 20b
a A LaTex expression showing 4square root of 2b
b A LaTex expression showing square root of b
c A LaTex expression showing 2square root of 5b
d A LaTex expression showing 2square root of 2b
e A LaTex expression showing 2square root of 3{b to the power of 3 }
f A LaTex expression showing square root of 8{b to the power of 3 }
4
Simplify the radical
A LaTex expression showing square root of 18y
a A LaTex expression showing square root of y
b A LaTex expression showing 6square root of 2y
c A LaTex expression showing square root of {y to the power of 3 }
d A LaTex expression showing 5square root of {y to the power of 3 }
e A LaTex expression showing 3square root of 2y
f A LaTex expression showing 5square root of y
5
Simplify the radical
A LaTex expression showing square root of 48n
a A LaTex expression showing 7square root of 4n
b A LaTex expression showing 2square root of 6n
c A LaTex expression showing 6square root of 6n
d A LaTex expression showing 4square root of 3n
e A LaTex expression showing square root of 5n
f A LaTex expression showing square root of 3n
6
Simplify the radical
A LaTex expression showing square root of 176{c to the power of 3 }
a A LaTex expression showing {c} to the power of 2 square root of 13c
b A LaTex expression showing 4csquare root of 11c
c A LaTex expression showing 6{c} to the power of 2 square root of 8{c to the power of 3 }
d A LaTex expression showing 7csquare root of 7c
e A LaTex expression showing 2csquare root of 14c
f A LaTex expression showing 7csquare root of 11c
7
Simplify the radical
A LaTex expression showing square root of 80{d to the power of 4 }
a A LaTex expression showing 5{d} to the power of 4 square root of 7
b A LaTex expression showing 5{d} to the power of 4 square root of 4
c A LaTex expression showing 4{d} to the power of 2 square root of 5
d A LaTex expression showing 3dsquare root of 6
e A LaTex expression showing 2dsquare root of 4
f A LaTex expression showing 4{d} to the power of 4 square root of 8