Question

find one rational and one irrational number between root2 and root3​

Answer 1

Answer:

2.5 and 2.14114111411114.....

Step-by-step explanation:

this question is simple........

for an irrational number u need to just write a number in a particular pattern other than the recurring pattern

Answer 2

Question :

Find an rational number between ✓2 and ✓3

Answer :

We know that ,

To find an rational number between any two numbers " a " and " b "

we can use the formula ,

$\frac{a + b}{2}$

Hence, using the above mentioned formula we can find a rational number between root 2 and root 3

Therefore,

An Rational number between ✓2 and ✓3 is

$\sqrt{2} \: and \: \sqrt{3} \\ \frac{ \sqrt{2} + \sqrt{3} }{2}$

As we know ,

✓2 = 1.414

✓3 = 1.732

Now substitute this value in the above formula ,

$\frac{1.414 + 1.732}{2} \\ \\ = \frac{3.146}{2} \\ \\ = 1.573 \\ \\ = 1.5 \: or \: \frac{3}{2} (approximately)$

Question :

Find an irrational number between ✓2 and ✓3

Answer :

We know that ,

To find an irrational number between any two numbers " a " and " b "

we can use the formula ,

$\sqrt{a \times b}$

Hence, using the above mentioned formula we can find a irrational number between root 2 and root 3

Therefore,

An Irrational number between ✓2 and ✓3 is

$\sqrt{2} \: and \: \sqrt{3} \\ = \sqrt{ \sqrt{2} \times \sqrt{3} } \\ = \sqrt{ \sqrt{6} } \\ = ( \sqrt{6} {)}^{ \frac{1}{2} } \\ = (6 {)}^{ \frac{1}{4} }$