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

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Radicals - Square - Simplifying, Values and Variables, Radical Remaining
1
Simplify the radical
A LaTex expression showing square root of 28{y to the power of 5 }
a A LaTex expression showing 2{y} to the power of 2 square root of 7y
b A LaTex expression showing 3ysquare root of 4y
c A LaTex expression showing 5ysquare root of 3y
d A LaTex expression showing {y} to the power of 2 square root of 3y
e A LaTex expression showing {y} to the power of 4 square root of 6{y to the power of 3 }
2
Simplify the radical
A LaTex expression showing square root of 44{b to the power of 4 }
a A LaTex expression showing {b} to the power of 3 square root of 13
b A LaTex expression showing 2{b} to the power of 2 square root of 12
c A LaTex expression showing 5{b} to the power of 4 square root of 13
d A LaTex expression showing 5{b} to the power of 4 square root of 7
e A LaTex expression showing 2{b} to the power of 2 square root of 11
3
Simplify the radical
A LaTex expression showing square root of 12{r to the power of 2 }
a A LaTex expression showing rsquare root of 6
b A LaTex expression showing rsquare root of 3
c A LaTex expression showing 3rsquare root of 6
d A LaTex expression showing r
e A LaTex expression showing 2rsquare root of 3
4
Simplify the radical
A LaTex expression showing square root of 32{p to the power of 2 }
a A LaTex expression showing 4psquare root of 5
b A LaTex expression showing 5{p} to the power of 2
c A LaTex expression showing 4{p} to the power of 2 square root of 2
d A LaTex expression showing 4p
e A LaTex expression showing 4psquare root of 2
5
Simplify the radical
A LaTex expression showing square root of 75{m to the power of 4 }
a A LaTex expression showing 8m
b A LaTex expression showing 6{m} to the power of 3 square root of 5
c A LaTex expression showing 5{m} to the power of 2 square root of 3
d A LaTex expression showing 8{m} to the power of 3 square root of 5
e A LaTex expression showing 7{m} to the power of 4 square root of 5
6
Simplify the radical
A LaTex expression showing square root of 275{y to the power of 2 }
a A LaTex expression showing 2ysquare root of 9
b A LaTex expression showing 4{y} to the power of 2 square root of 14
c A LaTex expression showing 4ysquare root of 8
d A LaTex expression showing 8ysquare root of 13
e A LaTex expression showing 5ysquare root of 11
7
Simplify the radical
A LaTex expression showing square root of 112{y to the power of 4 }
a A LaTex expression showing 4{y} to the power of 2 square root of 7
b A LaTex expression showing 2{y} to the power of 2 square root of 10
c A LaTex expression showing 7{y} to the power of 4 square root of 8
d A LaTex expression showing 3ysquare root of 9
8
Simplify the radical
A LaTex expression showing square root of 99{d to the power of 5 }
a A LaTex expression showing {d} to the power of 3 square root of 7d
b A LaTex expression showing 6dsquare root of 10d
c A LaTex expression showing 3{d} to the power of 2 square root of 11d
d A LaTex expression showing 4dsquare root of 7{d to the power of 2 }
e A LaTex expression showing 5dsquare root of 7d