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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Number of Factor Using Prime Factorization Method

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

Find the Smallest Square Root of the Square Number 252
2252
2126
363
321
77
1

Here, prime factor 7 has no pair.

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

(ii) 2925

Find the Smallest Square Root of the Number 2925
32925
3975
5325
565
1313
1

Here, prime factor 13 has no pair.

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

(iii) 396

Find the Smallest Square Root of the Number 396
2396
2198
399
333
1111
1

Here, prime factor 11 has no pair.

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

(iv) 2645

Find the Smallest Square Root of the Number 2645
52645
23529
2323
1

Here, prime factor 5 has no pair.

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

(v) 2800

Find the Square Roots 2800 for Squares and Square Root
22800
21400
2700
2350
5175
535
77
1

Here, prime factor 7 has no pair.

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

And

(vi) 1620

Find the Square Roots 1620 for Squares and Square Root
21620
2810
3405
3135
345
315
55
1

Here, prime factor 5 has no pair.

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

And

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