Division with Common Factor - 1 Term over 2 Terms to Fraction (Level 1)

This math topic focuses on simplifying radical expressions, particularly involving the division of one radical term over a sum of two radical terms to a fraction. Skills practiced include identifying and simplifying expressions with common radical factors, applying properties of radicals, and rationalizing denominators. Problems involve choices between multiple solutions, aiding in understanding the simplification processes for radical expressions. This is part of a broader practice of simplifying radicals.

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

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Radicals - Division with Common Factor - 1 Term over 2 Terms to Fraction Worksheet

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Radicals - Division with Common Factor - 1 Term over 2 Terms to Fraction
1
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 75}{square root of 27 + square root of 75}
a A LaTex expression showing 1 over 6
b A LaTex expression showing 5 over 4
c A LaTex expression showing 2 over 3
d A LaTex expression showing 5 over 8
e A LaTex expression showing 9 over 7
2
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 99}{square root of 44 + square root of 99}
a A LaTex expression showing 3 over 4
b A LaTex expression showing 3 over 7
c A LaTex expression showing 1 over 6
d A LaTex expression showing 1 over 10
e A LaTex expression showing 3 over 5
3
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 12}{square root of 12 + square root of 75}
a A LaTex expression showing 2 over 7
b A LaTex expression showing 5 over 17
c A LaTex expression showing 5 over 8
d A LaTex expression showing 1 over 16
e A LaTex expression showing 1 over 6
4
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 28}{square root of 28 + square root of 28}
a A LaTex expression showing 2 over 7
b A LaTex expression showing 5 over 8
c A LaTex expression showing 1 over 3
d A LaTex expression showing 1 over 2
e A LaTex expression showing 2 over 5
5
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 8}{square root of 18 + square root of 50}
a A LaTex expression showing 1 over 6
b A LaTex expression showing 3 over 7
c A LaTex expression showing 1 over 4
d A LaTex expression showing 5 over 8
e A LaTex expression showing 3 over 16
6
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 50}{square root of 8 + square root of 50}
a A LaTex expression showing 11 over 17
b A LaTex expression showing 5 over 8
c A LaTex expression showing 3 over 4
d A LaTex expression showing 5 over 7
e A LaTex expression showing 3 over 17
7
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 28}{square root of 63 + square root of 28}
a A LaTex expression showing 1 over 10
b A LaTex expression showing 2 over 13
c A LaTex expression showing 2 over 5
d A LaTex expression showing 2 over 3
e A LaTex expression showing 3 over 13
8
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 18}{square root of 8 + square root of 18}
a A LaTex expression showing 3 over 8
b A LaTex expression showing 1 over 2
c A LaTex expression showing 2 over 9
d A LaTex expression showing 3 over 7
e A LaTex expression showing 3 over 5