Question

find an irrational numbers between 5/ 7 and7/9 how many more they may be
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Answer 1

Answer:-

We know that, an irrational number between two given rational numbers is in the form of √ab where a and b are given numbers.

a = 5/7 and b = 7/9

One rational number = √5/7 × 7/9 = √5/9

Infinite number of irrational numbers will be in between two given numbers 5/7 and 7/9.

★ Alternative:-

→ Divide 5/7 & 7/9

→ 5/7 = 0.714258...... .

→ 7/9 = 0.777777........

Irrational numbers are:-

→ 0.720720072000720000......

→ 0.7340734007340007340000........

→ 0.740740074000740000........

→ 0.7567056700567000.....

$\bigstar$ Hence, proved!

Answer 2

Given

Two fraction

$\frac{5}{7}$ & $\frac{7}{9}$

To find

irrational no between these no

Solution

1. First step dividing the no
2. write the no in decimal like(2.455....)
3. when we in write in decimal the no is not finite
4. write the no's which is come between dividing no..

Dividing $\frac{5}{7}$

$\frac{5}{7}$ =0.7142857635373...

Dividing $\frac{7}{9}$

$\frac{7}{9}$= 0.7777777777777.....

• For more information this is repeating no

Now finding the no

1. 0.8836636373838...
2. 08452637367373...
3. 0.852626252553...

There is infinite irrational no we find from any two different rational no.