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

This math topic focuses on simplifying radical expressions involving the division of two terms each containing a combination of two square roots, and rewriting them as a single fraction. The expressions covered in the exercises typically involve simplifying square roots and common factors in both the numerator and denominator. Each problem is structured as a multiple-choice question, requiring students to select the correct simplified form of the given radical expression from several options. The problems are a part of a broader unit on simplifying radicals, aiming to enhance students' skills in handling and simplifying expressions containing square roots.

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

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Radicals - Division with Common Factor - 2 Terms over 2 Terms to Fraction
1
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 12 + square root of 12}{square root of 75 + square root of 12}
a A LaTex expression showing 3 over 10
b A LaTex expression showing 1 over 7
c A LaTex expression showing 2 over 15
d A LaTex expression showing 1 over 3
e A LaTex expression showing 4 over 7
2
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 50 + square root of 50}{square root of 18 + square root of 50}
a A LaTex expression showing 8 over 11
b A LaTex expression showing 1 over 3
c A LaTex expression showing 9 over 7
d A LaTex expression showing 5 over 4
e A LaTex expression showing 5 over 2
3
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 98 + square root of 50}{square root of 8 + square root of 8}
a A LaTex expression showing 21 over 11
b A LaTex expression showing 19 over 4
c A LaTex expression showing 3
d A LaTex expression showing 1 over 3
e A LaTex expression showing 11 over 4
4
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 27 + square root of 75}{square root of 75 + square root of 12}
a A LaTex expression showing 5 over 7
b A LaTex expression showing 5 over 11
c A LaTex expression showing 2
d A LaTex expression showing 8 over 7
e A LaTex expression showing 5 over 4
5
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 27 + square root of 12}{square root of 147 + square root of 12}
a A LaTex expression showing 5 over 9
b A LaTex expression showing 10 over 9
c A LaTex expression showing 5 over 4
d A LaTex expression showing 1 over 9
e A LaTex expression showing 1 over 2
6
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 8 + square root of 8}{square root of 98 + square root of 18}
a A LaTex expression showing 4 over 21
b A LaTex expression showing 8 over 3
c A LaTex expression showing 2 over 17
d A LaTex expression showing 7 over 13
e A LaTex expression showing 2 over 5
7
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 99 + square root of 44}{square root of 99 + square root of 99}
a A LaTex expression showing 4 over 5
b A LaTex expression showing 5 over 6
c A LaTex expression showing 1 over 2
d A LaTex expression showing 1 over 8
e A LaTex expression showing 1
8
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 20 + square root of 20}{square root of 125 + square root of 125}
a A LaTex expression showing 2
b A LaTex expression showing 2 over 5
c A LaTex expression showing 1
d A LaTex expression showing 1 over 9
e A LaTex expression showing 1 over 3