From the pairs of numbers given below, pick out those whose product is a natural number or a fraction. i. √3, √(12)

Question

From the pairs of numbers given below, pick out those whose product is a natural number or a fraction.

i. √3, \(\sqrt{12}\)

ii. √3, \(\sqrt{1.2}\)

iii. √5, √8

iv. \(\sqrt{0.5}\), √8

v. \(\sqrt{7\frac12}\), \(\sqrt{3}\frac13\)

Answer 1

i. \(\sqrt{3},\) \(\sqrt{12}\)

\(\sqrt{3}\) x \(\sqrt{12}\) = \(\sqrt{3}\times12=\sqrt{36}=6\)

product is natural number

ii. \(\sqrt{3},\) \(\sqrt{1.}2\)

\(\sqrt{3}\times\sqrt{1.}2\) = \(\sqrt{3}\times1.2\) = \(\sqrt{3.6}\)

product is neither a natural number nor a fraction

iii. \(\sqrt{3},\) \(\sqrt{8}\)

\(\sqrt{5}\times\sqrt{8}\) = \(\sqrt{5}\times 8\) = \(\sqrt{40}\)

product is neither a natural number nor a fraction

iv. \(\sqrt{0.5},\) \(\sqrt{8}\)

\(\sqrt{0.5}\times\sqrt{8}\) = \(\sqrt{0.5}\times8\) = \(\sqrt{4}\) = 2

product is natural number

v. \(\sqrt{7\frac{1}{2}},\) \(\sqrt{3}\frac{1}{3}\)

product is natural number