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Question

2 rational numbers between √2 and √3


Solution

For rational number:

√2= 1.414 (up to 3 places after decimal place)

√3= 1.732 ( “ “ “ “ )

So, there may be so many rational numbers we can get . Consider for first place of decimal place and if we place the numbers in the number line we see 1.5 is one rational number [3/2] lies in between 1.4 and 1.7. As,

√2<1.5<√3

And other number is 1.7 means 17/10 which is also a rational number between 1.414(up to 3 places after decimal) and 1.732(up to 3 places after decimal)

For irrational number.

We know , both √2 & √3 are irrational number.

So √2+√3 ¡s also irrational. Therefore(√2+√3)/2 is also irrational number. As ,

√2<(√2+√3)/2 <√3, (√2+√3)/2 is one irrational number between √2 &√3.

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