CBSE Class 10-Mathematics: Chapter –1 Real Numbers Part 9

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Question 5:

Prove that product of three consecutive positive integers is divisible by 6.

Answer:

Let three consecutive numbers be and

Let

Product of

Which is divisible by

Which is divisible by

Which is divisible by

Which is divisible by

Which is divisible by

Question 6:

Prove that is an irrational number.

Answer:

Let

are integers, so is a rational number, but is an irrational number. This contradiction arises because of our wrong assumption.

So is an irrational number.

Question 7:

Prove that if and are odd positive integers, then is even but not divisible by .

Answer:

Let and

is an even number but not divisible

Question 8:

Show that one and only one out of is divisible by , where .

Answer:

Let the number be

then, numbers are

is divisible by

then, numbers are

is divisible by

If then, numbers are

is divisible

Out of only one is divisible