# NCERT Class 8 Mathematics Solutions: Chapter 6 – Squares and Square Roots Exercise 6.3 Part 5 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question: 6** For each of the following numbers find the smallest whole number by which it should be divided so as to get a perfect square. Also, find the square root of the square number so obtained:

(i) 252

(ii) 2925

(iii) 396

(iv) 2645

(v) 2800

(vi) 1620

**Answer**:

**(i)** 252

2 | 252 |

2 | 126 |

3 | 63 |

3 | 21 |

7 | 7 |

1 |

Here, prime factor 7 has no pair.

Therefore 252 must be divided by 7 to make it a perfect square.

**(ii)** 2925

3 | 2925 |

3 | 975 |

5 | 325 |

5 | 65 |

13 | 13 |

1 |

Here, prime factor 13 has no pair.

Therefore 2925 must be divided by 13 to make it a perfect square.

**(iii)** 396

2 | 396 |

2 | 198 |

3 | 99 |

3 | 33 |

11 | 11 |

1 |

Here, prime factor 11 has no pair.

Therefore 396 must be divided by 11 to make it a perfect square.

**(iv)** 2645

5 | 2645 |

23 | 529 |

23 | 23 |

1 |

Here, prime factor 5 has no pair.

Therefore 2645 must be divided by 5 to make it a perfect square.

**(v)** 2800

2 | 2800 |

2 | 1400 |

2 | 700 |

2 | 350 |

5 | 175 |

5 | 35 |

7 | 7 |

1 |

Here, prime factor 7 has no pair.

Therefore 2800 must be divided by 7 to make it a perfect square.

And

**(vi)** 1620

2 | 1620 |

2 | 810 |

3 | 405 |

3 | 135 |

3 | 45 |

3 | 15 |

5 | 5 |

1 |

Here, prime factor 5 has no pair.

Therefore 1620 must be divided by 5 to make it a perfect square.

And