Question

Find two irrational number between 0.3 and 0.7

Answer 1

Use the property of geometric means. Between any 2 numbers aa and bb, provided abab is not a perfect square, ab−−√ab is an irrational number.

In your case, ab=0.7×0.77=0.539ab=0.7×0.77=0.539. So 0.539−−−−√0.539 is one irrational number.

For the other irrational number, your choices are 0.7×0.539−−−−√−−−−−−−−−−√0.7×0.539 or 0.77×0.539−−−−√−−−−−−−−−−−√0.77×0.539.

N.B.: After finding0.539−−−−√0.539 as the first irrational number, you can also find the arithmetic mean of 0.70.7 (or 0.770.77) and 0.539−−−−√0.539. They are possible answers too!

Hope it helps you
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Answer 2

Answer:

1/√10 and 1/√5 will do

Step-by-step explanation:

0.3 < x < 0.7

<=> 0.09 < x² < 0.49

So just choose two nonsquares in this interval and then take their square roots.

Say

√0.1 = 1/√10

and

√0.2 = 1/√5