Question

(√5 - √2)² is ______
(a) a natural number
(b) an irrational number
(c) a whole number
(d) a rational number

Answer 1

Irrational number is your answer. Lets the root3+root5!^2 be rational number root3^2+2*root3*root5+root5^2=p/q 3+2root15+5=p/q 8+2root15=p/q root15=p-8/2q.

Here p,q,-8,2arerational numbers and we know that root15 is an irrational number and (root3+root5)^2 is not a rational number.

Overall this contradiction has arisen as our assumption is wrong. Hence (√3+√5)² is an irrational number

Answer 2

Hi ,

Given ( √5 - √2 )²

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We know the algebraic identity :

( a - b )² = a² + b² - 2ab

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Now ,

( √5 - √2 )²

= (√5)² + (√2)² - 2 × √5 × √2

= 5 + 2 - 2√10

= 7 - 2√10 ( An irrational number )

Therefore ,

Option ( b ) is correct.

I hope this helps you.

: )