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

This math topic focuses on simplifying radicals which involve division, specifically one term over two terms converted to fractions. Benchmark proficiency is required in simplifying radical expressions by factoring out common factors, rationalizing denominators, and reducing expressions to simplest form. Each problem presents a radical division query and multiple choice answers. The learners are encouraged to simplify each expression thoroughly to arrive at the correct fraction form. This is part of a broader practice on 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 27}{square root of 147 + square root of 12}
a A LaTex expression showing 1 over 11
b A LaTex expression showing 4 over 7
c A LaTex expression showing 1 over 16
d A LaTex expression showing 1 over 3
e A LaTex expression showing 1 over 4
2
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 75}{square root of 75 + square root of 27}
a A LaTex expression showing 9 over 5
b A LaTex expression showing 1 over 2
c A LaTex expression showing 5 over 8
d A LaTex expression showing 1 over 7
3
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 98}{square root of 50 + square root of 50}
a A LaTex expression showing 5 over 7
b A LaTex expression showing 3 over 20
c A LaTex expression showing 5 over 6
d A LaTex expression showing 11 over 7
e A LaTex expression showing 7 over 10
4
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 18}{square root of 8 + square root of 50}
a A LaTex expression showing 2 over 3
b A LaTex expression showing 3 over 16
c A LaTex expression showing 3 over 7
d A LaTex expression showing 1 over 7
e A LaTex expression showing 7 over 10
5
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 125}{square root of 125 + square root of 20}
a A LaTex expression showing 9 over 8
b A LaTex expression showing 1
c A LaTex expression showing 4 over 7
d A LaTex expression showing 5 over 7
e A LaTex expression showing 5 over 4
6
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 147}{square root of 12 + square root of 75}
a A LaTex expression showing 1 over 17
b A LaTex expression showing 14 over 5
c A LaTex expression showing 15 over 17
d A LaTex expression showing 5 over 2
e A LaTex expression showing 1
7
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 18}{square root of 50 + square root of 8}
a A LaTex expression showing 3 over 7
b A LaTex expression showing 4 over 3
c A LaTex expression showing 1 over 3
d A LaTex expression showing 7 over 16
e A LaTex expression showing 5 over 9
8
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 45}{square root of 45 + square root of 125}
a A LaTex expression showing 4 over 7
b A LaTex expression showing 5 over 19
c A LaTex expression showing 1 over 11
d A LaTex expression showing 3 over 8