Division with Mixed Index and Power of Radicand (Fraction) - Radical over Radical (Level 2)

This math topic centers on simplifying radical expressions involving various complexities such as division of radicals with different indices and radicand powers. It mainly focuses on handling radical divisions where both the numerator and denominator are radicals, often expressed in fractional form. The challenges involve computing expressions with mixed indices and manipulating powers of radicands, which helps in mastering the rules for simplifying such expressions. These problems are integral to developing proficiency in handling advanced radical operations. Each problem presents a radical expression and requires simplifying it to its simplest form, with multiple choice answers provided.

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

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Radicals - Division with Mixed Index and Power of Radicand (Fraction) - Radical over Radical Worksheet

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Radicals - Division with Mixed Index and Power of Radicand (Fraction) - Radical over Radical
1
What does this radical expression simplify to?
A LaTex expression showing \frac{2-th root of 81 to the power of 2 }{3-th root of 216 to the power of 2 }
a A LaTex expression showing 9 over 4
b A LaTex expression showing 163 over 74
c A LaTex expression showing 1 over 10
d A LaTex expression showing 78 over 5
e A LaTex expression showing 31 over 9
2
What does this radical expression simplify to?
A LaTex expression showing \frac{3-th root of 9 to the power of 3 }{2-th root of 16 to the power of 2 }
a A LaTex expression showing 7 over 26
b A LaTex expression showing 1 over 2
c A LaTex expression showing 9 over 16
d A LaTex expression showing 5 over 9
e A LaTex expression showing 4 over 7
3
What does this radical expression simplify to?
A LaTex expression showing \frac{3-th root of 8 to the power of 4 }{2-th root of 64 to the power of 2 }
a A LaTex expression showing 23 over 59
b A LaTex expression showing 5 over 113
c A LaTex expression showing 1 over 4
d A LaTex expression showing 18 over 131
e A LaTex expression showing 11 over 106
4
What does this radical expression simplify to?
A LaTex expression showing \frac{2-th root of 64 to the power of 2 }{3-th root of 25 to the power of 3 }
a A LaTex expression showing 1 over 3
b A LaTex expression showing 64 over 25
c A LaTex expression showing 49 over 20
d A LaTex expression showing 1
e A LaTex expression showing 23
5
What does this radical expression simplify to?
A LaTex expression showing \frac{3-th root of 125 to the power of 2 }{2-th root of 16 to the power of 3 }
a A LaTex expression showing 51 over 35
b A LaTex expression showing 25 over 64
c A LaTex expression showing 49 over 117
d A LaTex expression showing 19 over 75
e A LaTex expression showing 23 over 43
6
What does this radical expression simplify to?
A LaTex expression showing \frac{2-th root of 16 to the power of 2 }{3-th root of 4 to the power of 3 }
a A LaTex expression showing 26 over 5
b A LaTex expression showing 4
c A LaTex expression showing 17 over 5
d A LaTex expression showing 2 over 5
e A LaTex expression showing 5 over 4
7
What does this radical expression simplify to?
A LaTex expression showing \frac{2-th root of 64 to the power of 2 }{3-th root of 8 to the power of 2 }
a A LaTex expression showing 64 over 5
b A LaTex expression showing 16
c A LaTex expression showing 80 over 11
d A LaTex expression showing 7 over 4
e A LaTex expression showing 127 over 8
8
What does this radical expression simplify to?
A LaTex expression showing \frac{3-th root of 4 to the power of 3 }{2-th root of 64 to the power of 2 }
a A LaTex expression showing 2 over 23
b A LaTex expression showing 7 over 52
c A LaTex expression showing 1 over 16
d A LaTex expression showing 1 over 5
e A LaTex expression showing 4 over 7