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)

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

### Find a rational between root2 and root3 (√2and√3) ?

Answer is 1.5

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