Square - Simplifying, Values and Variables, Nothing Remaining (Level 3)

This math topic focuses on advanced simplification of square roots involving both constants and variables. It involves problems where students are required to simplify radicals that contain perfect squares and power of variables, ensuring that the simplified form has no radical remnants. Each problem presents multiple choice answers, challenging students to determine the correct simplified form of radical expressions. This practice enhances skills in identifying and simplifying square roots, handling exponents, and applying basic algebraic rules in the context of 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, Nothing Remaining Worksheet

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Radicals - Square - Simplifying, Values and Variables, Nothing Remaining
1
Simplify the radical
A LaTex expression showing square root of 4{p to the power of 2 {c} to the power of 2 }
a A LaTex expression showing 4pcsquare root of 3
b A LaTex expression showing 2pc
c A LaTex expression showing pc
d A LaTex expression showing {p} to the power of 3 {c} to the power of 2
e A LaTex expression showing pcsquare root of 2
2
Simplify the radical
A LaTex expression showing square root of 4{m to the power of 2 {d} to the power of 4 }
a A LaTex expression showing 5{m} to the power of 3 d
b A LaTex expression showing 2m{d} to the power of 2
c A LaTex expression showing md
d A LaTex expression showing {m} to the power of 3 d
3
Simplify the radical
A LaTex expression showing square root of 16{y to the power of 4 {d} to the power of 4 }
a A LaTex expression showing 2y{d} to the power of 3 square root of 4
b A LaTex expression showing 7{y} to the power of 4 {d} to the power of 2 square root of 2
c A LaTex expression showing 4{y} to the power of 3 dsquare root of 2
d A LaTex expression showing 4{y} to the power of 2 {d} to the power of 2
e A LaTex expression showing 5y{d} to the power of 2 square root of 2
4
Simplify the radical
A LaTex expression showing square root of 16{x to the power of 4 {d} to the power of 4 }
a A LaTex expression showing {x} to the power of 2 {d} to the power of 2 square root of 3
b A LaTex expression showing 4{x} to the power of 2 {d} to the power of 2
c A LaTex expression showing 6{x} to the power of 3 dsquare root of 3
d A LaTex expression showing {x} to the power of 4 d
e A LaTex expression showing x{d} to the power of 3 square root of 2
5
Simplify the radical
A LaTex expression showing square root of 25{x to the power of 2 {c} to the power of 4 }
a A LaTex expression showing 7x{c} to the power of 3
b A LaTex expression showing 6{x} to the power of 2 {c} to the power of 4
c A LaTex expression showing 8x{c} to the power of 4
d A LaTex expression showing 3x{c} to the power of 3
e A LaTex expression showing 5x{c} to the power of 2
6
Simplify the radical
A LaTex expression showing square root of 9{m to the power of 2 {x} to the power of 4 }
a A LaTex expression showing {m} to the power of 2 x
b A LaTex expression showing {m} to the power of 3 {x} to the power of 3
c A LaTex expression showing {m} to the power of 3 {x} to the power of 2 square root of 3
d A LaTex expression showing 3m{x} to the power of 2
e A LaTex expression showing 3mx
7
Simplify the radical
A LaTex expression showing square root of 9{d to the power of 2 {p} to the power of 4 }
a A LaTex expression showing 6dp
b A LaTex expression showing {d} to the power of 2 p
c A LaTex expression showing 4d{p} to the power of 4
d A LaTex expression showing 3d{p} to the power of 2
e A LaTex expression showing 2{d} to the power of 2 p
8
Simplify the radical
A LaTex expression showing square root of 9{n to the power of 4 {c} to the power of 4 }
a A LaTex expression showing 3{n} to the power of 3 c
b A LaTex expression showing 6{n} to the power of 4 {c} to the power of 3
c A LaTex expression showing n{c} to the power of 3 square root of 3
d A LaTex expression showing 3{n} to the power of 2 {c} to the power of 2
e A LaTex expression showing 4nc