Question

State whether the following statements are true or false. Justify your answers.
(i) Every irrational number is a real number.
(ii) Every point on the number line is of the form, where m is a natural number.
(iii) Every real number is an irrational number.

Answer 1

1)true because real number are divided into rational and irrational numbers o every irrational number is a real number
2)true
3)false because as reals have rational no also so every irrational number is not a real number

Answer 2

Irrational numbers:

The numbers which cannot be expressed in the form p/q, where p & q both are integers and q≠0 , are called irrational numbers. e.g √2, √ 3, π e.t.c

Real numbers:

The collection of all rational and irrational numbers together form a collection of real numbers. Every real number can be represented by a unique point on the number line. Also, every point on the number line represents a unique real number.

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Solution:

i) TRUE,
Real numbers= rational numbers + irrational numbers

ii) FALSE,
Because no negative number can be the square root of any natural number.

iii) FALSE,
Because rational numbers are also present in the collection of real numbers.

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