NCERT Class 8 Mathematics Solutions: Chapter 6 – Squares and Square Roots Exercise 6.3 Part 5

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Number of factor using prime factorization method

Number of Factor Using Prime Factorization Method

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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

Find the smallest square root of the square number 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

Find the smallest square root of the number 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

Find the smallest square root of the number 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

Find the smallest square root of the number 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

Find the Square Roots 2800 for Squares and Square Root

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

Find the Square Roots 1620 for Squares and Square Root

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