Answer :

First we square the two given numbers

0.7^{2} = 0.49

0.77^{2} = 0.5929

Square root of any two non perfect square numbers between 0.49 and 0.5929 will give an irrational number since they are not perfect squares.

√0.5 = 0.7071067811…

√0.53 = 0.728010988…

So √0.5 and √0.53 are the two irrational numbers between 0.7 and 0.77

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