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

Step-by-step explanation:

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Answer 2

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

A) 5+ √5

B) (2+ √5 )√5

C) (2 + √5 )(2 - √5)

D) 5√5

Solution :-

A) 5 + √5 = 5 + 2.23606797.. = 7.23606797..

• Since, decimal representation of this number is non-terminating, it is an irrational number.

B) (2 + √5)√5

→ 2√5 + 5

→ 2*2.23606797.. + 5

→ irrational + rational

→ irrational number.

C) (2 + √5)(2 - √5)

using (a + b)(a - b) = a² - b² ,

→ (2)² - (√5)²

→ 4 - 5

→ (-1)

→ (-1)/1

• The above number can be represented as p/q, where both p and q are integers, this number is a rational number.

D) 5√5

→ 5 * √5

→ rational * irrational

→ irrational number.

Hence, (C) (2 + √5)(2 - √5) is not an irrational number.

Learn more :-

given that under root 3 is irrational prove that 5 root 3 minus 2 is an irrational number

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