Math, asked by raginishahdeo711, 9 hours ago

answer only if u can ??
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Answered by MrImpeccable
78

ANSWER:

To Do:

  • Find 2 irrational numbers for each of the following case, that satisfy them.

Solution:

1. Two Irrational numbers whose difference is an irrational number.

1 + √8 & 1 - √8

Proof:

⇒ Difference of 1 + √8 & 1 - √8 = 1 + √8 - 1 + √8 =2√8 = Irrational Number.

(1 + √8 & 1 - √8 are irrational numbers)

2. Two Irrational numbers whose difference is a rational number.

⇒ √8 + 1 & √8 - 1

Proof:

⇒ Difference of √8 + 1 & √8 - 1 - √8 = √8 - 1 - √8 + 1 = 2 = Rational Number.

( √8 + 1 & √8 - 1 are irrational numbers)

3. Two Irrational numbers whose sum is an irrational number.

⇒ √8 + 1 & √8 - 1

Proof:

⇒ Sum of √8 + 1 & √8 - 1 = √8 - 1 + √8 - 1 = 2√8 = Irrational Number.

(√8 + 1 & √8 - 1 are irrational numbers)

4. Two Irrational numbers whose sum is a rational number.

⇒ 1 + √8 & 1 - √8

Proof:

⇒ Sum of 1 + √8 & 1 - √8 = 1 + √8 + 1 - √8 = 2 = Rational Number.

(1 + √8 & 1 - √8 are irrational numbers)

5. Two Irrational numbers whose product is an irrational number.

⇒ √2 & √3

Proof:

⇒ Product of √2 & √3 = √2 × √3 = √6 = Irrational Number.

(√2 & √3 are irrational numbers)

6. Two Irrational numbers whose product is a rational number.

⇒ √8 & √2

Proof:

⇒ Product of √8 & √2 = √8 × √2 = √16 = 4 = Rational Number.

(√8 & √2 are irrational numbers)

7. Two Irrational numbers whose quotient is an irrational number.

⇒ √6 & √2

Proof:

⇒ Quotient of √6 & √2 = √6/√2 = √3 = Irrational Number.

(√6 & √2 are irrational numbers)

8. Two Irrational numbers whose quotient is a rational number.

⇒ √8 & √2

Proof:

⇒ Quotient of √8 & √2 = √8/√2 = √4 = 2 = Rational Number.

(√8 & √2 are irrational numbers)

Learn More:

  • Irrational Numbers: Numbers which cannot be represented in p/q forms.
  • Eg: √2, √3, etc.
Answered by Anonymous
3

hope it helps !!

thnku

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