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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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 50{n to the power of 2 }
a A LaTex expression showing 2n
b A LaTex expression showing 8n
c A LaTex expression showing 3{n} to the power of 2
d A LaTex expression showing 5nsquare root of 2
2
Simplify the radical
A LaTex expression showing square root of 176x
a A LaTex expression showing 5square root of 10x
b A LaTex expression showing 5square root of 12x
c A LaTex expression showing square root of 12x
d A LaTex expression showing 4square root of 11x
e A LaTex expression showing square root of 14{x to the power of 2 }
3
Simplify the radical
A LaTex expression showing square root of 175p
a A LaTex expression showing 2square root of 9p
b A LaTex expression showing 5square root of 7p
c A LaTex expression showing 5square root of 9p
d A LaTex expression showing 7square root of 9p
e A LaTex expression showing 2square root of 3{p to the power of 3 }
4
Simplify the radical
A LaTex expression showing square root of 125{r to the power of 2 }
a A LaTex expression showing 4rsquare root of 2
b A LaTex expression showing 6rsquare root of 5
c A LaTex expression showing {r} to the power of 2 square root of 2
d A LaTex expression showing 5rsquare root of 5
e A LaTex expression showing 4r
5
Simplify the radical
A LaTex expression showing square root of 8{x to the power of 3 }
a A LaTex expression showing {x} to the power of 3 square root of 4{x to the power of 3 }
b A LaTex expression showing xsquare root of x
c A LaTex expression showing 2xsquare root of 2x
d A LaTex expression showing {x} to the power of 2 square root of x
e A LaTex expression showing 4xsquare root of 5x
6
Simplify the radical
A LaTex expression showing square root of 12d
a A LaTex expression showing square root of 3{d to the power of 2 }
b A LaTex expression showing 2square root of d
c A LaTex expression showing square root of 2d
d A LaTex expression showing 2square root of 3d
e A LaTex expression showing 4square root of 6{d to the power of 3 }
7
Simplify the radical
A LaTex expression showing square root of 275z
a A LaTex expression showing 4square root of 8{z to the power of 3 }
b A LaTex expression showing 8square root of 7z
c A LaTex expression showing 5square root of 11z
d A LaTex expression showing 5square root of 12z
e A LaTex expression showing 8square root of 9{z to the power of 2 }