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

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Simplify the radical

63c3\sqrt{63{c}^{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 1)'. 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 8{r to the power of 2 }
a A LaTex expression showing rsquare root of 2
b A LaTex expression showing 2rsquare root of 2
c A LaTex expression showing {r} to the power of 2 square root of 4
d A LaTex expression showing 3rsquare root of 5
e A LaTex expression showing rsquare root of 3
f A LaTex expression showing 2rsquare root of 4
2
Simplify the radical
A LaTex expression showing square root of 44x
a A LaTex expression showing 5square root of 8x
b A LaTex expression showing square root of 13{x to the power of 3 }
c A LaTex expression showing 4square root of 8{x to the power of 3 }
d A LaTex expression showing 2square root of 10{x to the power of 2 }
e A LaTex expression showing square root of 9{x to the power of 3 }
f A LaTex expression showing 2square root of 11x
3
Simplify the radical
A LaTex expression showing square root of 27{z to the power of 2 }
a A LaTex expression showing 6zsquare root of 6
b A LaTex expression showing 6{z} to the power of 3 square root of 2
c A LaTex expression showing 4{z} to the power of 3 square root of 2
d A LaTex expression showing 4z
e A LaTex expression showing 4{z} to the power of 3
f A LaTex expression showing 3zsquare root of 3
4
Simplify the radical
A LaTex expression showing square root of 48{y to the power of 3 }
a A LaTex expression showing 7ysquare root of 6{y to the power of 2 }
b A LaTex expression showing 7ysquare root of y
c A LaTex expression showing 2ysquare root of 5y
d A LaTex expression showing {y} to the power of 2 square root of 2y
e A LaTex expression showing 4ysquare root of 3y
f A LaTex expression showing ysquare root of 5{y to the power of 3 }
5
Simplify the radical
A LaTex expression showing square root of 18{x to the power of 2 }
a A LaTex expression showing 5xsquare root of 4
b A LaTex expression showing 3xsquare root of 2
c A LaTex expression showing x
d A LaTex expression showing 5{x} to the power of 2
e A LaTex expression showing xsquare root of 4
f A LaTex expression showing {x} to the power of 2 square root of 5
6
Simplify the radical
A LaTex expression showing square root of 12{x to the power of 3 }
a A LaTex expression showing xsquare root of 5{x to the power of 2 }
b A LaTex expression showing 2xsquare root of 3x
c A LaTex expression showing 4{x} to the power of 2 square root of 5x
d A LaTex expression showing {x} to the power of 3 square root of 4{x to the power of 2 }
e A LaTex expression showing 3xsquare root of x
f A LaTex expression showing 2{x} to the power of 2 square root of 2{x to the power of 2 }
7
Simplify the radical
A LaTex expression showing square root of 275{z to the power of 3 }
a A LaTex expression showing 7{z} to the power of 3 square root of 8z
b A LaTex expression showing 5{z} to the power of 3 square root of 13z
c A LaTex expression showing 4zsquare root of 7{z to the power of 2 }
d A LaTex expression showing 5zsquare root of 11z
e A LaTex expression showing 2{z} to the power of 2 square root of 7z
f A LaTex expression showing 2{z} to the power of 2 square root of 11{z to the power of 2 }