Rewriting Roots (Level 4)

This math topic focuses on practicing complex numbers, specifically rewriting roots as complex numbers and simplifying radicals. Each problem presents a unique expression involving a square root of a negative product, which needs to be expressed in terms of complex numbers (using the imaginary unit \(i\)). It enhances understanding of the fundamental concepts of complex numbers and the manipulation of expressions involving powers and roots. The problems progressively build skills in simplifying and rewriting complex expressions in clearer forms and algebraic manipulation involving imaginary numbers.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Complex Numbers - Rewriting Roots Worksheet

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Complex Numbers - Rewriting Roots
1
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -63r{z to the power of 4 }
a A LaTex expression showing zisquare root of 4r
b A LaTex expression showing 2{z} to the power of 3 isquare root of 9r
c A LaTex expression showing zisquare root of 9r
d A LaTex expression showing {z} to the power of 3 isquare root of 9r
e A LaTex expression showing zisquare root of 5{r to the power of 2 }
f A LaTex expression showing 3{z} to the power of 2 isquare root of 7r
2
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -63{y to the power of 2 x}
a A LaTex expression showing 3yisquare root of 7x
b A LaTex expression showing 2yisquare root of 9x
c A LaTex expression showing 3yisquare root of 9x
d A LaTex expression showing yisquare root of 8x
e A LaTex expression showing {y} to the power of 2 isquare root of 10x
f A LaTex expression showing 5yisquare root of 7{x to the power of 2 }
3
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -18y{m to the power of 3 }
a A LaTex expression showing 3misquare root of ym
b A LaTex expression showing misquare root of ym
c A LaTex expression showing 3misquare root of 2ym
d A LaTex expression showing {m} to the power of 3 isquare root of 2{y to the power of 2 m}
e A LaTex expression showing 4misquare root of ym
f A LaTex expression showing 2{m} to the power of 2 isquare root of {y to the power of 2 m}
4
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -125{b to the power of 2 {c} to the power of 3 }
a A LaTex expression showing 8bcisquare root of 2{c to the power of 3 }
b A LaTex expression showing bcisquare root of 4c
c A LaTex expression showing 5bcisquare root of 5c
d A LaTex expression showing 2bcisquare root of 5c
e A LaTex expression showing 4{b} to the power of 3 cisquare root of 8{c to the power of 3 }
f A LaTex expression showing 3b{c} to the power of 3 isquare root of 2{c to the power of 2 }
5
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -27y{z to the power of 4 }
a A LaTex expression showing 4{z} to the power of 3 isquare root of y
b A LaTex expression showing 3{z} to the power of 2 isquare root of 3y
c A LaTex expression showing 4{z} to the power of 3 isquare root of 2y
d A LaTex expression showing {z} to the power of 2 isquare root of 4{y to the power of 2 }
e A LaTex expression showing 4{z} to the power of 3 isquare root of {y to the power of 3 }
f A LaTex expression showing 6{z} to the power of 2 isquare root of {y to the power of 2 }
6
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -112c{n to the power of 4 }
a A LaTex expression showing 4{n} to the power of 2 isquare root of 7c
b A LaTex expression showing 7nisquare root of 8c
c A LaTex expression showing 2nisquare root of 3c
d A LaTex expression showing 7{n} to the power of 3 isquare root of 8c
e A LaTex expression showing 2{n} to the power of 2 isquare root of 3c
f A LaTex expression showing 6{n} to the power of 4 isquare root of 10c
7
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -20{r to the power of 3 {p} to the power of 4 }
a A LaTex expression showing rpisquare root of 5{r to the power of 2 }
b A LaTex expression showing {r} to the power of 3 pisquare root of 4{r to the power of 2 }
c A LaTex expression showing 4r{p} to the power of 3 isquare root of 5r
d A LaTex expression showing {r} to the power of 3 {p} to the power of 3 isquare root of 4r
e A LaTex expression showing 2r{p} to the power of 2 isquare root of 5r
f A LaTex expression showing 2{r} to the power of 3 pisquare root of r
8
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -63b{p to the power of 3 }
a A LaTex expression showing 3pisquare root of 7bp
b A LaTex expression showing {p} to the power of 2 isquare root of 10{b to the power of 3 {p} to the power of 2 }
c A LaTex expression showing 2{p} to the power of 2 isquare root of 8b{p to the power of 3 }
d A LaTex expression showing pisquare root of 7b{p to the power of 3 }
e A LaTex expression showing 2pisquare root of 4{b to the power of 2 p}
f A LaTex expression showing pisquare root of 7{b to the power of 2 p}