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2022 AMC 10B Question 5

AMC10 · 2022 AMC 10B

Question 5

What is the value of $$
\frac{\left(1+\frac{1}{3}\right)\left(1+\frac15\right)\left(1+\frac17\right)}{\sqrt{\left(1-\frac{1}{3^2}\right)\left(1-\frac{1}{5^2}\right)\left(1-\frac{1}{7^2}\right)}}?
$$
  1. $ \sqrt3 $
  2. $ 2 $
  3. $ \sqrt{15} $
  4. $ 4 $
  5. $ \sqrt{105} $