Insert a rational and an irrational number between $2$ and $3$ .

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Solution

We know, if $a$ and $b$ are the two rational numbers, then a rational number between them can be $\frac{a + b}{2}$
and irrational number is $\sqrt{a b}$ , provided $a b$ is not a perfect square.

Then, a rational number between $2$ and $3 = \frac{2 + 3}{2} = \frac{5}{2} = 2.5$ .

An irrational number between $2$ and $3$ is $\sqrt{2 \times 3} = \sqrt{6}$ .

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Similar questions

(a) Find ten rational number between - $\frac{2}{5}$ and $\frac{1}{2}$ .

(b) Insert 5 rational numbers and 2 irrational numbers between $\sqrt{2}$ and $\sqrt{3}$ .

[4 MARKS]

Q. Question 3
Insert a rational number and an irrational number between the following
(i) 2 and 3
(ii) 0 and 0.1
(iii)

\frac{1}{3}

and

\frac{1}{2}

(iv)

\frac{- 2}{5}

and

\frac{1}{2}

(v) 0.15 and 0.16
(vi)

\sqrt{2}

and

\sqrt{3}

(vii) 2.357 and 3.121
(viii) .0001 and .001
(ix) 3.623623 and 0.484848
(x) 3.375289 and 6.375738

Q. Insert five irrational numbers between

2 \sqrt{5}

and

3 \sqrt{3}

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Insert a rational and an irrational number between 2 and 3.

We know, if a and b are the two rational numbers, then a rational number between them can be a+b2 and irrational number is √ab, provided ab is not a perfect square.Then, a rational number between 2 and 3=2+32=52=2.5.An irrational number between 2 and 3 is √2×3=√6 .

Insert a rational and an irrational number between $2$ and $3$ .