Question

match each irrational number with another irrational number so that the product of the two numbers is rational.

\\(\sqrt{6}\\)
\\(\sqrt{20}\\)
\\(\sqrt{2}\\)
\\(\sqrt{3}\\)

options to match:
\\(\sqrt{32}\\), \\(\sqrt{5}\\), \\(\sqrt{\frac{1}{10}}\\), \\(\pi\\), \\(\sqrt{6}\\), \\(\sqrt{7}\\), \\(\sqrt{12}\\)

Explanation:

Step1: Match \(\sqrt{6}\)

$$\sqrt{6} \times \sqrt{6} = 6$$

Step2: Match \(\sqrt{20}\)

$$\sqrt{20} \times \sqrt{5} = \sqrt{100} = 10$$

Step3: Match \(\sqrt{2}\)

$$\sqrt{2} \times \sqrt{32} = \sqrt{64} = 8$$

Step4: Match \(\sqrt{3}\)

$$\sqrt{3} \times \sqrt{12} = \sqrt{36} = 6$$

Answer:

• \(\sqrt{6}\) matches with \(\sqrt{6}\)
• \(\sqrt{20}\) matches with \(\sqrt{5}\)
• \(\sqrt{2}\) matches with \(\sqrt{32}\)
• \(\sqrt{3}\) matches with \(\sqrt{12}\)