NCERT Class 8 Mathematics Solutions: Chapter 6 – Squares and Square Roots Exercise 6.3 Part 4 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Prime Factor of Numbers

Question: 5 For each of the following numbers find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also, find the square root of the square number so obtained:

(i) 252

(ii) 180

(iii) 1008

(iv) 2028

(v) 1458

(vi) 768

Answer:

(i) 252

Find the Square Roots of 252
2252
2126
363
321
77
1

Here, prime factor 7 has no pair.

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

(ii) 180

Find the Square Roots of 180
2180
290
345
315
55
1

Here, prime factor 5 has no pair.

Therefore 180 must be multiplied by 5 to make it a perfect square.

(iii) 1008

Find the Square Roots of 1008
21008
2504
2252
2126
363
321
77
1

Here, prime factor 7 has no pair.

Therefore 1008 must be multiplied by 7 to make it a perfect square.

(iv) 2028

Find the Square Roots of 2028
22028
21014
3507
13169
1313
1

Here, prime factor 3 has no pair.

Therefore 2028 must be multiplied by 3 to make it a perfect square.

(v) 1458

Find the Square Roots of 1458
21458
3729
3243
381
327
39
33
1

Here, prime factor 2 has no pair.

Therefore 1458 must be multiplied by 3 to make it a perfect square.

(vi) 768

Find the Square Roots of 768
2768
2384
2192
296
248
224
212
26
33
1

Here, prime factor 3 has no pair.

Therefore 768 must be multiplied by 3 to make it a perfect square.