Question

show that ,(√5-√2) (√5+√2) is a rational number

Answer 1

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(√5-√2) (√5+√2)

Using the identity :

$(a + b)(a - b) = {a}^{2} + {b}^{2}$

We get :

${( \sqrt{5} )}^{2} + {( \sqrt{2} )}^{2}$

$= 5 + 2$

= 7, which is a rational number

So, (√5-√2) (√5+√2) is a rational number.

Answer 2

Answer:

Simplifying it, we get:

(√5-√2) (√5+√2)

=> 5 - 2 [using the formula = (a + b) (a - b) = a^2 - b^2]

=> 3

since 3 is a rational number,

(√5-√2) (√5+√2) is also a rational number.

Hope it Helps!!