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Question Number 165511 by MathsFan last updated on 02/Feb/22

 how do i find an irrational  number between  0.124  and  0.125

$$\:\boldsymbol{{how}}\:\boldsymbol{{do}}\:\boldsymbol{{i}}\:\boldsymbol{{find}}\:\boldsymbol{{an}}\:\boldsymbol{{irrational}} \\ $$$$\boldsymbol{{number}}\:\boldsymbol{{between}}\:\:\mathrm{0}.\mathrm{124}\:\:\boldsymbol{{and}} \\ $$$$\mathrm{0}.\mathrm{125} \\ $$

Commented by Rasheed.Sindhi last updated on 02/Feb/22

Particularly in this case:  (√(0.124×0.125))

$${Particularly}\:{in}\:{this}\:{case}: \\ $$$$\sqrt{\mathrm{0}.\mathrm{124}×\mathrm{0}.\mathrm{125}} \\ $$

Commented by mr W last updated on 03/Feb/22

for example  ((a+b)/2)±(((a−b))/(2(√2)))  ((a+b)/2)±(((a−b))/(2(√3)))  ((a+b)/2)±(((a−b))/(2(√5)))  .....  with a,b =rational numbers

$${for}\:{example} \\ $$$$\frac{{a}+{b}}{\mathrm{2}}\pm\frac{\left({a}−{b}\right)}{\mathrm{2}\sqrt{\mathrm{2}}} \\ $$$$\frac{{a}+{b}}{\mathrm{2}}\pm\frac{\left({a}−{b}\right)}{\mathrm{2}\sqrt{\mathrm{3}}} \\ $$$$\frac{{a}+{b}}{\mathrm{2}}\pm\frac{\left({a}−{b}\right)}{\mathrm{2}\sqrt{\mathrm{5}}} \\ $$$$..... \\ $$$${with}\:{a},{b}\:={rational}\:{numbers} \\ $$

Commented by MathsFan last updated on 03/Feb/22

thank you

$${thank}\:{you} \\ $$

Commented by MathsFan last updated on 03/Feb/22

thank you sir

$${thank}\:{you}\:{sir} \\ $$

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