Question

If a and b are natural numbers, then (√a + √b) ( √a - √b) is rational, Is it True? - Justify your answer​

Answer 1

Answer

Yes,Because__(√a+√b)(√a-√b) = (√a)²-(√b)² = a-b__ which is going to be a rational number because difference of two rational numbers is rational.

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Answer 2

Answer:

False

Step-by-step explanation:

$\frac{\sqrt{a}+\sqrt{b}}{\sqrt{a}-\sqrt{b}}$

$\frac{\sqrt{a}+\sqrt{b}}{\sqrt{a}-\sqrt{b}}×\frac{\sqrt{a}+{\sqrt{b}}{\sqrt{a}+\sqrt{b}}$

$\frac{(\sqrt{a}+\sqrt{b})²}{(\sqrt{a})²-(\sqrt{b})²}$

$\frac{\sqrt{a}+\sqrt{b}}{\sqrt{a}-\sqrt{b}}=\frac{a+b+2\sqrt{ab}}{a-b}$

As √ab is not a rational number for all natural numbers a and b

So, $\frac{\sqrt{a}+\sqrt{b}}{\sqrt{a}-sqrt{b}}$ is not a rational number

Hence,

The statement is "false".