how to solve root 10 and 7.3 on number line

Consider a number line. Let the point O represent 0 and point A represent 3.

Now draw a perpendicular AP at A on the number line and cut off arc AB = 1 unit.

Using Pythagoras Theorem, we have

With O as the centre and

as radius draw an arc cutting real line at C. Clearly,

Thus, C represents on the number line.

Now let us find the square root of 7.3

Make a list of perfect squares, 0, 4, 9, 16, 25, 36, …

Identify perfect squares closest to 7.3

Thus we have, 4 < 7.3 < 9

Take a positive square root of each number.

Thus, we have

Now evaluate the square roots.

Therefore, we have,

Now make a list of perfect squares between 2 and 3.

Numbers | Squares |
---|---|

2.1 | 4.41 |

2.2 | 4.84 |

2.3 | 5.29 |

2.4 | 5.76 |

2.5 | 6.25 |

2.6 | 6.76 |

2.7 | 7.29 |

2.8 | 7.84 |

2.9 | 8.41 |

Thus, from the list it is clear that, 7.29 is closer to 7.3.

Therefore, we have,

Thus, we can mark 2.7 on the number line as follows:

Thus, OA represents the square root of 7.3