Square - Simplifying, Values and Variables, Radical Remaining (Level 1)

This math topic focuses on simplifying square roots involving numerical and variable expressions. It includes problems where learners need to simplify radical expressions to their simplest form, often resulting in a mixture of integer coefficients, variables under the radical sign, or entirely removed from the radical. The radicals contain a combination of perfect squares and non-perfect squares, both with and without variables raised to various powers. These problems help to strengthen skills in identifying factors within radicands, using properties of exponents and radicals effectively, and simplifying complex algebraic expressions involving radicals.

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 175p
a A LaTex expression showing 5square root of 7p
b A LaTex expression showing 2square root of 9p
c A LaTex expression showing 5square root of 9p
d A LaTex expression showing 2square root of 3{p to the power of 3 }
e A LaTex expression showing 7square root of 9p
2
Simplify the radical
A LaTex expression showing square root of 50{r to the power of 2 }
a A LaTex expression showing 5rsquare root of 2
b A LaTex expression showing 2{r} to the power of 3 square root of 3
c A LaTex expression showing 5rsquare root of 5
d A LaTex expression showing {r} to the power of 2
e A LaTex expression showing 5rsquare root of 3
3
Simplify the radical
A LaTex expression showing square root of 50{z to the power of 2 }
a A LaTex expression showing {z} to the power of 2 square root of 3
b A LaTex expression showing 4z
c A LaTex expression showing 6z
d A LaTex expression showing 5zsquare root of 2
e A LaTex expression showing 6{z} to the power of 2 square root of 5
4
Simplify the radical
A LaTex expression showing square root of 75{p to the power of 2 }
a A LaTex expression showing 8{p} to the power of 2
b A LaTex expression showing 3{p} to the power of 3
c A LaTex expression showing 5psquare root of 3
d A LaTex expression showing 6p
e A LaTex expression showing 2psquare root of 2
5
Simplify the radical
A LaTex expression showing square root of 12d
a A LaTex expression showing 4square root of 6{d to the power of 3 }
b A LaTex expression showing square root of 2d
c A LaTex expression showing 2square root of 3d
d A LaTex expression showing 2square root of d
e A LaTex expression showing square root of 3{d to the power of 2 }
6
Simplify the radical
A LaTex expression showing square root of 112{z to the power of 2 }
a A LaTex expression showing 7zsquare root of 3
b A LaTex expression showing 5zsquare root of 4
c A LaTex expression showing 4zsquare root of 7
d A LaTex expression showing {z} to the power of 3 square root of 7
7
Simplify the radical
A LaTex expression showing square root of 27c
a A LaTex expression showing 6square root of {c to the power of 2 }
b A LaTex expression showing 3square root of 3c
c A LaTex expression showing square root of 2c
d A LaTex expression showing square root of 6{c to the power of 3 }
e A LaTex expression showing square root of 2{c to the power of 3 }
8
Simplify the radical
A LaTex expression showing square root of 75{r to the power of 2 }
a A LaTex expression showing {r} to the power of 2
b A LaTex expression showing 6rsquare root of 3
c A LaTex expression showing 5rsquare root of 3
d A LaTex expression showing 3rsquare root of 5
e A LaTex expression showing 4rsquare root of 3