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A) $\sqrt {\text{5}} {\text{,}}\sqrt {\text{2}} $

B) $\sqrt {\text{8}} {\text{,}}\sqrt {\text{2}} $

C) $\sqrt {\text{3}} {\text{,}}\sqrt {\text{2}} $

D) $\sqrt 7 {\text{,}}\sqrt {\text{2}} $

Answer

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If two rational number on dividing has a rational number as the quotient one must a rational multiple of another. For example, a and b are two irrational numbers and on dividing has a rational number as the quotient then,

${\text{a = rb}}$ where, ${\text{r}} \in {\text{Q}}$

On dividing $\sqrt {\text{5}} {\text{ and }}\sqrt {\text{2}} $, we get either $\dfrac{{\sqrt {\text{5}} }}{{\sqrt {\text{2}} }}{\text{ or }}\dfrac{{\sqrt {\text{2}} }}{{\sqrt {\text{5}} }}$ and neither is a rational number.

From option(B)

On dividing $\sqrt {\text{8}} {\text{ and }}\sqrt {\text{2}} $, we get either $\dfrac{{\sqrt {\text{8}} }}{{\sqrt {\text{2}} }}{\text{ = 2 or }}\dfrac{{\sqrt {\text{2}} }}{{\sqrt {\text{8}} }}{\text{ = }}\dfrac{{\text{1}}}{{\text{2}}}$ and both are rational number.

From option(C)

On dividing $\sqrt {\text{3}} {\text{ and }}\sqrt {\text{2}} $, we get either $\dfrac{{\sqrt {\text{3}} }}{{\sqrt {\text{2}} }}{\text{ or }}\dfrac{{\sqrt {\text{2}} }}{{\sqrt {\text{3}} }}$ and neither is a rational number.

From option(C)

On dividing $\sqrt {\text{7}} {\text{ and }}\sqrt {\text{2}} $, we get either $\dfrac{{\sqrt {\text{7}} }}{{\sqrt {\text{2}} }}{\text{ or }}\dfrac{{\sqrt {\text{2}} }}{{\sqrt {\text{7}} }}$ and neither is a rational number.