The number that will be perfectly divisible by each one of 4, 9, and 10 is their LCM. The LCM of these numbers is as follows.

2 | 4, 9, 10 |

2 | 2, 9, 5 |

3 | 1, 9, 5 |

3 | 1, 3, 5 |

5 | 1, 1, 5 |

| 1, 1, 1 |

LCM of 4, 9, 10 = __2 × 2__ × __3 × 3 __× 5 =180

Here, prime factor 5 does not have its pair. Therefore, 180 is not a perfect square. If we multiply 180 with 5, then the number will become a perfect square. Therefore, 180 should be multiplied with 5 to obtain a perfect square.

Hence, the required square number is 180 × 5 = 900