Rewriting Roots (Level 3)

This math topic focuses on advanced manipulation of complex numbers, specifically the skill of rewriting square roots that contain negative radicands into complex number expressions. Students are encouraged to simplify such expressions and manage radicals effectively, integrating both imaginary units and variable exponents. The problems involve interpreting and transforming complex algebraic structures that include powers and roots into their simplified complex forms. This is an advanced exercise aimed at deepening understanding of complex numbers and their properties in the context of algebra.

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 -75{c to the power of 4 }
a A LaTex expression showing 5{c} to the power of 2 isquare root of 3
b A LaTex expression showing 2cisquare root of 2
c A LaTex expression showing 2{c} to the power of 2 i
d A LaTex expression showing 3{c} to the power of 4 i
e A LaTex expression showing 5cisquare root of 3
f A LaTex expression showing cisquare root of 2
2
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -44{p to the power of 3 }
a A LaTex expression showing pisquare root of 13{p to the power of 3 }
b A LaTex expression showing {p} to the power of 2 isquare root of 9{p to the power of 3 }
c A LaTex expression showing pisquare root of 12p
d A LaTex expression showing pisquare root of 9p
e A LaTex expression showing 2pisquare root of 11p
f A LaTex expression showing 3pisquare root of 13p
3
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -12{z to the power of 2 }
a A LaTex expression showing 2zisquare root of 3
b A LaTex expression showing 3zisquare root of 3
c A LaTex expression showing {z} to the power of 2 isquare root of 2
d A LaTex expression showing 2{z} to the power of 2 isquare root of 5
e A LaTex expression showing 4{z} to the power of 2 isquare root of 4
f A LaTex expression showing zisquare root of 5
4
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -32{d to the power of 3 }
a A LaTex expression showing 7{d} to the power of 2 isquare root of {d to the power of 3 }
b A LaTex expression showing 5{d} to the power of 3 isquare root of d
c A LaTex expression showing 4disquare root of 2d
d A LaTex expression showing 3disquare root of 2d
e A LaTex expression showing 4{d} to the power of 3 isquare root of d
f A LaTex expression showing 6{d} to the power of 3 isquare root of 2d
5
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -80{p to the power of 2 }
a A LaTex expression showing 4pisquare root of 5
b A LaTex expression showing 2pi
c A LaTex expression showing 2pisquare root of 4
d A LaTex expression showing 3pisquare root of 6
e A LaTex expression showing {p} to the power of 3 isquare root of 4
f A LaTex expression showing 3pi
6
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -20{n to the power of 4 }
a A LaTex expression showing nisquare root of 7
b A LaTex expression showing 5{n} to the power of 4 isquare root of 3
c A LaTex expression showing 2{n} to the power of 2 isquare root of 5
d A LaTex expression showing 3{n} to the power of 2 isquare root of 5
e A LaTex expression showing nisquare root of 8
f A LaTex expression showing {n} to the power of 2 isquare root of 4
7
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -20{b to the power of 4 }
a A LaTex expression showing bisquare root of 5
b A LaTex expression showing 2{b} to the power of 2 isquare root of 5
c A LaTex expression showing 5{b} to the power of 3 isquare root of 4
d A LaTex expression showing bisquare root of 6
e A LaTex expression showing {b} to the power of 4 isquare root of 4
f A LaTex expression showing 5bisquare root of 6
8
Rewrite the root as a complex number and simplify all radicals
A LaTex expression showing square root of -80{b to the power of 4 }
a A LaTex expression showing {b} to the power of 2 isquare root of 6
b A LaTex expression showing 4{b} to the power of 2 isquare root of 5
c A LaTex expression showing 6{b} to the power of 3 isquare root of 4
d A LaTex expression showing 7{b} to the power of 4 isquare root of 7
e A LaTex expression showing 3bisquare root of 3
f A LaTex expression showing 6bisquare root of 6