Question

write an example of two irrational numbers whose product is a rational number ​

Answer 1

Answer:

Given:

Any two irrational numbers

To show:

that the product is rational .

Solving Question:

we can take any two irrational number and multiply it to show this.

Rational number : a number which can be written in the form of p/q, where q≠0

Irrational number: a number which cannot be written in the form of p/q, where q≠0

Solution:

There are many irrational numbers which could suit this question

Let us consider this example : √2 and 2√2 , they are irrational as they have √2

Multiply it ,

⇒ 2√2 * √2

or , 2 * 2 = 4 [ as √2 * √2 = 2 ]

Clearly 4 is a rational number.

Next example , take √15 and √60

Simplify √60

⇒ √60 = √4*15

or, 2√15

multiply the both number

⇒ 2√15 * √25

or, 2* √15 *√15

or, 2* 15

or, 30

we, know that 30 is a rational number hence we proved it

Answer 2

Answer:

Given:

Any two irrational numbers

To show:

that the product is rational .

Solving Question:

we can take any two irrational number and multiply it to show this.

Rational number : a number which can be written in the form of p/q, where q≠0

Irrational number: a number which cannot be written in the form of p/q, where q≠0

Solution:

There are many irrational numbers which could suit this question

Let us consider this example : √2 and 2√2 , they are irrational as they have √2

Multiply it ,

⇒ 2√2 * √2

or , 2 * 2 = 4 [ as √2 * √2 = 2 ]

Clearly 4 is a rational number.

Next example , take √15 and √60

Simplify √60

⇒ √60 = √4*15

or, 2√15

multiply the both number

⇒ 2√15 * √25

or, 2* √15 *√15

or, 2* 15

or, 30

we, know that 30 is a rational number hence we proved it