Question

2. ਇਹਨਾਂ ਵਿੱਚੋਂ ਕਿਹੜੀ ਅਪਰਿਮੇਯ ਸੰਖਿਆ ਨਹੀਂ ਹੈ?
Which of the following is not an
irrational number? निम्नलिखित में से कौन
सी एक अपरिमेय संख्या नहीं है?​

Answer 1

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

As we know,

• Rational + Irrational = Irrational

we have,

• 5 = Rational .
• √5 = Irrational .

So,

→ 5+ √5

→ Rational + Irrational = Irrational .

B) (2 - √5)√5

As we know ,

• Rational * Irrational = Irrational.

So,

→ (2+ √5 )√5

→ 2√5 + 5

• 2 = Rational.
• √5 = Irrational.

then,

→ 2 * √5

→ Rational * Irrational

→ 2√5 Irrational

Now,

→ Rational + Irrational = Irrational

→ 2√5 + 5

→ Irrational

C) (2 + √5 )(2 - √5)

using ,

• (a + b)(a - b) = a² - b²

→ (2 + √5 )(2 - √5)

→ (2)² - (√5)²

→ 4 - 5

→ -1

→ (-1)/1 in form of p/q, where q ≠ 0 ,

So,

• (2 + √5 )(2 - √5) is a Rational Number.

D) 5√5

• √5 = Irrational
• 5 = Rational

then,

→ 5 * √5

→ Rational * Irrational

→ Irrational

→ 5√5

→ Irrational .

Hence, (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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