State whether x = 2.23.....+ 3/4 is rational or not.
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x = 2.23....... + 3/4
x = irrational + 3/4 ( since the decimal expansion 2.23..... is non-terminating and also non-repeating )
x = irrational + rational ( since 3/4 = 0.75 which is terminating )
therefore, x = irrational ( as sum of irrational and rational no.s is irrational )
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