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A pair of irrational numbers whose product is a rational number is:

(A) \((\sqrt{16}, \sqrt 5)\)

(B) \((\sqrt{5}, \sqrt 2)\)

(C) \((\sqrt 3, \sqrt {27})\)

(D) \((\sqrt {36}, \sqrt 2)\)

1 Answer

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Best answer

Correct option is (C) \((\sqrt{3}, \sqrt {27})\) 

(A) \((\sqrt{16}, \sqrt 5)\)

\(= \sqrt {16} \times \sqrt 5\)

\(= 4\sqrt 5\)

(B) \((\sqrt{5}, \sqrt 2)\)

\(= \sqrt 5 \times \sqrt 2\)

\(= \sqrt {10}\)

(C) \((\sqrt 3, \sqrt {27})\)

\(=\sqrt 3 \times \sqrt{27}\)

\( =\sqrt{3} \times 3 \sqrt {3}\)

\(= 3\times 3\)

\(= 9\)

(D) \((\sqrt {36}, \sqrt 2)\)

\(= \sqrt{36 } \times\sqrt2\)

\(= 6\sqrt2\)

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