If a and b are both positive rational numbers, then ( a + b ) ( a… - Vidyadip

MCQ

If $a$ and $b$ are both positive rational numbers, then $\big(\sqrt{\text{a}}+\sqrt{\text{b}}\big)\big(\sqrt{\text{a}}-\sqrt{\text{b}}\big)$ is :

A
neither rational nor rational number
B
none of these
C
an irrational number
✓
a rational number

✓

Answer

Correct option: D.

a rational number

$\bigg(\sqrt{\text{a}}+\sqrt{\text{b}}\bigg)\bigg(\sqrt{\text{a}}-\sqrt{\text{b}}\bigg)$
$=\Big\{(\sqrt{\text{a}})^2-\big(\sqrt{\text{b}})^2\Big\}$
$= (a - b)$
Since $a$ and $b$ both are positive rational numbers,
Therefore, the difference of two positive rational numbers is also rational.

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