Question

Assertion: the product of (5+√5) and (3-√5) is an irrational number. Reason: the product of two irrational number is always a rational number​

Answer 1

Answer:

assertion is true but reason is false.

Answer 2

Solution :-

Assertion: the product of (5+√5) and (3-√5) is an irrational number

checking,

→ (5 + √5) * (3 - √5)

→ 5 * 3 - 5√5 + 3√5 - √5 * √5

→ 15 - 2√5 - 5

→ 10 - 2√5

now,

• The square root of a non perfect square number is always irrational => √5 is irrational .
• Rational * irrational = Irrational => 2 * √5 = Irrational .
• Rational - Irrational = Irrational => 10 - 2√5 = Irrational .

Therefore, we can conclude that,

• Assertion is True .

Reason: the product of two irrational number is always a rational number .

Example (1) :-

→ √2 = Irrational

So,

→ √2 * √2 = 2

→ Irrational * Irrational = Rational number .

Example (2) :-

→ √2 = Irrational

→ √8 = Irrational

So,

→ √2 * √8 = √16 = 4

→ Irrational * Irrational = Rational number .

Example (3) :-

→ √3 = Irrational

→ √27 = Irrational

So,

→ √3 * √27 = √81 = 9

→ Irrational * Irrational = Rational number .

Therefore, we can conclude that,

• Reason is False .

Learn more :-

prove that √2-√5 is an irrational number

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