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

This math topic involves simplifying radical expressions which appear as ratios involving sums of square roots in both the numerator and the denominator. The problems require finding common factors and practicing the manipulation of surds to simplify the expressions into fractional forms. Each question includes multiple-choice answers, enhancing students' ability to solve and choose among potential simplifications of radical expressions involving terms like the square roots of numbers such as 8, 18, 20, 45, 50, and 98. This forms part of a broader unit focused on simplifying radicals.

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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 75 + square root of 75}{square root of 27 + square root of 27}
a A LaTex expression showing 5 over 9
b A LaTex expression showing 5 over 3
c A LaTex expression showing 13 over 9
d A LaTex expression showing 13 over 8
e A LaTex expression showing 5 over 7
2
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 12 + square root of 27}{square root of 27 + square root of 75}
a A LaTex expression showing 7 over 18
b A LaTex expression showing 5 over 8
c A LaTex expression showing 1
d A LaTex expression showing 9 over 4
3
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 8 + square root of 18}{square root of 50 + square root of 8}
a A LaTex expression showing 3 over 10
b A LaTex expression showing 3 over 16
c A LaTex expression showing 4 over 5
d A LaTex expression showing 7 over 3
e A LaTex expression showing 5 over 7
4
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 18 + square root of 50}{square root of 98 + square root of 18}
a A LaTex expression showing 9 over 14
b A LaTex expression showing 4 over 5
c A LaTex expression showing 4 over 3
d A LaTex expression showing 14 over 3
e A LaTex expression showing 8 over 13
5
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 20 + square root of 45}{square root of 20 + square root of 20}
a A LaTex expression showing 8 over 7
b A LaTex expression showing 1
c A LaTex expression showing 1 over 11
d A LaTex expression showing 5 over 4
e A LaTex expression showing 9 over 11
6
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 8 + square root of 50}{square root of 50 + square root of 18}
a A LaTex expression showing 6 over 7
b A LaTex expression showing 7 over 8
c A LaTex expression showing 7 over 15
d A LaTex expression showing 2 over 3
e A LaTex expression showing 11 over 13
7
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 20 + square root of 20}{square root of 45 + square root of 45}
a A LaTex expression showing 1
b A LaTex expression showing 2 over 15
c A LaTex expression showing 2 over 3
d A LaTex expression showing 1 over 3
e A LaTex expression showing 9 over 10
8
What does this radical expression simplify to?
A LaTex expression showing \frac{square root of 27 + square root of 27}{square root of 75 + square root of 75}
a A LaTex expression showing 8 over 9
b A LaTex expression showing 4 over 11
c A LaTex expression showing 2 over 3
d A LaTex expression showing 3 over 5
e A LaTex expression showing 3 over 7