Square - Simplifying, Values and Variables, Radical Remaining (Level 3)

This math topic focuses on advanced techniques for simplifying square roots involving radicals, particularly when dealing with algebraic expressions that include variables and coefficients. The problems require extracting perfect squares from under the radical and simplifying the remaining expressions. Each question presents a radical expression and multiple choice answers, challenging students to apply their skills in algebraic manipulation and understanding of radical properties to find the simplest form. The problems target an understanding of how to handle higher powers and coefficients within square roots effectively.

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 50{y to the power of 4 r}
a A LaTex expression showing 5{y} to the power of 2 square root of 2r
b A LaTex expression showing 2ysquare root of 4r
c A LaTex expression showing 7ysquare root of {r to the power of 3 }
d A LaTex expression showing 3{y} to the power of 3 square root of r
e A LaTex expression showing 3{y} to the power of 4 square root of 3r
2
Simplify the radical
A LaTex expression showing square root of 18{y to the power of 2 {b} to the power of 3 }
a A LaTex expression showing 4y{b} to the power of 3 square root of 3{b to the power of 2 }
b A LaTex expression showing 2{y} to the power of 2 {b} to the power of 2 square root of {b to the power of 3 }
c A LaTex expression showing 3ybsquare root of 2b
d A LaTex expression showing ybsquare root of {b to the power of 3 }
e A LaTex expression showing 4ybsquare root of 3b
3
Simplify the radical
A LaTex expression showing square root of 8b{x to the power of 3 }
a A LaTex expression showing xsquare root of b{x to the power of 2 }
b A LaTex expression showing 2xsquare root of 2bx
c A LaTex expression showing 2xsquare root of 3{b to the power of 3 {x} to the power of 3 }
d A LaTex expression showing xsquare root of 5bx
4
Simplify the radical
A LaTex expression showing square root of 32{r to the power of 5 {d} to the power of 5 }
a A LaTex expression showing 4{r} to the power of 3 dsquare root of {r to the power of 2 {d} to the power of 2 }
b A LaTex expression showing 4{r} to the power of 2 {d} to the power of 2 square root of 2rd
c A LaTex expression showing {r} to the power of 2 {d} to the power of 3 square root of 4rd
d A LaTex expression showing 4{r} to the power of 2 {d} to the power of 2 square root of rd
e A LaTex expression showing 4{r} to the power of 4 dsquare root of {r to the power of 3 d}
5
Simplify the radical
A LaTex expression showing square root of 27{b to the power of 4 x}
a A LaTex expression showing {b} to the power of 4 square root of 6x
b A LaTex expression showing 4{b} to the power of 2 square root of 4{x to the power of 2 }
c A LaTex expression showing bsquare root of 2x
d A LaTex expression showing 3{b} to the power of 2 square root of 3x
e A LaTex expression showing 2bsquare root of 5x
6
Simplify the radical
A LaTex expression showing square root of 20{x to the power of 5 {d} to the power of 4 }
a A LaTex expression showing {x} to the power of 4 {d} to the power of 2 square root of 2{x to the power of 3 }
b A LaTex expression showing 2{x} to the power of 2 {d} to the power of 2 square root of 5x
c A LaTex expression showing 3x{d} to the power of 3 square root of 6x
d A LaTex expression showing x{d} to the power of 3 square root of 3x
e A LaTex expression showing {x} to the power of 4 dsquare root of 7{x to the power of 2 }
7
Simplify the radical
A LaTex expression showing square root of 99{z to the power of 3 {m} to the power of 5 }
a A LaTex expression showing 6z{m} to the power of 4 square root of 12{z to the power of 2 {m} to the power of 3 }
b A LaTex expression showing 3z{m} to the power of 2 square root of 11zm
c A LaTex expression showing 5z{m} to the power of 2 square root of 9{z to the power of 3 {m} to the power of 2 }
d A LaTex expression showing zmsquare root of 13{z to the power of 2 {m} to the power of 2 }
e A LaTex expression showing {z} to the power of 3 {m} to the power of 4 square root of 7{z to the power of 2 {m} to the power of 3 }
8
Simplify the radical
A LaTex expression showing square root of 275{b to the power of 4 {d} to the power of 5 }
a A LaTex expression showing 4{b} to the power of 3 dsquare root of 14{d to the power of 3 }
b A LaTex expression showing 8bdsquare root of 7d
c A LaTex expression showing 4{b} to the power of 3 dsquare root of 11{d to the power of 3 }
d A LaTex expression showing 7b{d} to the power of 4 square root of 12d
e A LaTex expression showing 5{b} to the power of 2 {d} to the power of 2 square root of 11d