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Q1) Answer is (iv) √2 / 2 + √2 / 2
Q2) Answer is 8 : 3
Step-by-step explanation:
Q1) Evaluating each of them:
(i) ( 1 + √3 ) - ( √3 - 1 ) = 1 + √3 - √3 + 1 = 2, which is rational
(ii) 2 + 5√5 - √125 = 2 + 5√5 - √( 25×5 ) = 2 + 5√5 - √25√5 = 2 + 5√5 - 5√5 = 2, which is rational
(iii) π / 2π = 1 / 2, which is rational
(iv) √2 / 2 + √2 / 2 = √2 ( 1/2 + 1/2 ) = √2 × 1 = √2, which is irrational
Q2) 4√28 : 3√7
= 4√( 4 × 7 ) : 3√7
= 4√4√7 : 3√7
= 4×2√7 : 3√7
= 8√7 : 3√7
= 8 : 3
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