[Explained] Find a rational between root2 and root3

To find find a rational between root2 and root3 we need to be clear about the definition of Rational number

What is a rational number?

A rational number is a number that can be expressed in the form of x/y, where y must not be 0. (x and y being integer)

A rational number between √2 and √3 is 1.5

Let us understand with explanation.

Explanation:

If we divide a rational number we get a number in either repeating decimals or terminating decimals.

On expressing √2 in decimals we get non-recurring and non-terminating decimals as √2 is an irrational number.

Similarly, on expressing √3 in decimals we get non-recurring and non-terminating decimals as √3 is an irrational number.

√2 = 1.414 (rounded to 3 decimal places) and √3 = 1.732 (rounded to 3 decimal places).

Below are the 3 decimal places rounded numbers in between 1.414 and 1.732

1.414
1.415
1.416
1.417
1.418
1.419
1.42
1.421
1.422
1.423
1.424
1.425
1.426
1.427
1.428
1.429
1.43
1.431
1.432
1.433
1.434
1.435
1.436
1.437
1.438
1.439
1.44
1.441
1.442
1.443
1.444
1.445
1.446
1.447
1.448
1.449
1.45
1.451
1.452
1.453
1.454
1.455
1.456
1.457
1.458
1.459
1.46
1.461
1.462
1.463
1.464
1.465
1.466
1.467
1.468
1.469
1.47
1.471
1.472
1.473
1.474
1.475
1.476
1.477
1.478
1.479
1.48
1.481
1.482
1.483
1.484
1.485
1.486
1.487
1.488
1.489
1.49
1.491
1.492
1.493
1.494
1.495
1.496
1.497
1.498
1.499
1.5
1.501
1.502
1.503
1.504
1.505
1.506
1.507
1.508
1.509
1.51
1.511
1.512
1.513
1.514
1.515
1.516
1.517
1.518
1.519
1.52
1.521
1.522
1.523
1.524
1.525
1.526
1.527
1.528
1.529
1.53
1.531
1.532
1.533
1.534
1.535
1.536
1.537
1.538
1.539
1.54
1.541
1.542
1.543
1.544
1.545
1.546
1.547
1.548
1.549
1.55
1.551
1.552
1.553
1.554
1.555
1.556
1.557
1.558
1.559
1.56
1.561
1.562
1.563
1.564
1.565
1.566
1.567
1.568
1.569
1.57
1.571
1.572
1.573
1.574
1.575
1.576
1.577
1.578
1.579
1.58
1.581
1.582
1.583
1.584
1.585
1.586
1.587
1.588
1.589
1.59
1.591
1.592
1.593
1.594
1.595
1.596
1.597
1.598
1.599
1.6
1.601
1.602
1.603
1.604
1.605
1.606
1.607
1.608
1.609
1.61
1.611
1.612
1.613
1.614
1.615
1.616
1.617
1.618
1.619
1.62
1.621
1.622
1.623
1.624
1.625
1.626
1.627
1.628
1.629
1.63
1.631
1.632
1.633
1.634
1.635
1.636
1.637
1.638
1.639
1.64
1.641
1.642
1.643
1.644
1.645
1.646
1.647
1.648
1.649
1.65
1.651
1.652
1.653
1.654
1.655
1.656
1.657
1.658
1.659
1.66
1.661
1.662
1.663
1.664
1.665
1.666
1.667
1.668
1.669
1.67
1.671
1.672
1.673
1.674
1.675
1.676
1.677
1.678
1.679
1.68
1.681
1.682
1.683
1.684
1.685
1.686
1.687
1.688
1.689
1.69
1.691
1.692
1.693
1.694
1.695
1.696
1.697
1.698
1.699
1.7
1.701
1.702
1.703
1.704
1.705
1.706
1.707
1.708
1.709
1.71
1.711
1.712
1.713
1.714
1.715
1.716
1.717
1.718
1.719
1.72
1.721
1.722
1.723
1.724
1.725
1.726
1.727
1.728
1.729
1.73
1.731
1.732

This shows that there are many rational numbers between √2 and √3, for example, 1.5

Thus, a rational number between √2 and √3 is 1.5

So for the question

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