Question

Which of the following is not an irrational number? निम्नलिखित में से कौन सी एक अपरिमेय संख्या नहीं है? *

5+ √5

(2+ √5 )√5

(2 + √5 )(2 - √5)

5√5

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Answer 1

Answer:

(2+root 5) (2-root5)

Step-by-step explanation:

since it is in the formula of (a+b) (a-b) therefore answer is rational that is -1

Answer 2

Given : 5+ √5

(2+ √5 )√5

(2 + √5 )(2 - √5)

5√5

To Find : Which  is not an irrational number

Solution:

5+ √5

5 - Rational

√5 - Irrational

Rational + Irrational  = Irrational

=> 5+ √5  is Irrational  

(2+ √5 )√5

= 2√5 +  5

2 is rational  ,

√5  irrational

5 Rational

rational   x irrational = irrational  => 2√5  - irrational

Rational + Irrational  = Irrational  

=> 2√5 +  5  Irrational  

(2 + √5 )(2 - √5)

= 4 - 5

= - 1

Rational

5√5

√5  irrational

5 Rational

rational   x irrational = irrational  => 5√5  - irrational

5√5 irrational  

Only number which is not irrational is   (2 + √5 )(2 - √5)

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