Question

for each of the following numbers find the smallest natural number by which it should be multiplied so as to get a perfect square. Also find the square root of the square number so obtained 1]588 2]720 3]2178 4]3042 5]6300

Answer 1

Answer:

Step-by-step explanation:

Solution:

(i) 588 = 2 × 2 × 3 × 7 × 7

We know that

588/2 = 294/2 = 147/3 = 49/7 = 7/7 = 1

By pairing the same kind of factors, one factor 3 is left unpaired.

So to make it a pair we must multiply it by 3

Required least number = 3

Square root of 588 × 3 = 1764

Here

2 × 3 × 7 = 42

(ii) 720 = 2 × 2 × 2 × 2 × 3 × 3 × 5

We know that

720/2 = 360/2 = 180/2 = 90/2 = 45/3 = 15/3 = 5/5 = 1

By pairing the same kind of factors, one factor 5 is left unpaired.

So to make it a pair we must multiply it by 5

Required least number = 5

Square root of 720 × 5 = 3600

Here

2 × 2 × 3 × 5 = 60

(iii) 2178 = 2 × 3 × 3 × 11 × 11

We know that

2178/2 = 1089/3 = 363/3 = 121/11 = 11/11 = 1

By pairing the same kind of factors, one factor 2 is left unpaired.

So to make it a pair we must multiply it by 2

Required least number = 2

Square root of 2178 × 2 = 4356

Here

2 × 3 × 11 = 66

(iv) 3042 = 2 × 3 × 3 × 13 × 13

We know that

3042/2 = 1521/3 = 507/3 = 169/13 = 13/13 = 1

By pairing the same kind of factors, one factor 2 is left unpaired

So to make it a pair we must multiply it by 2

Required least number = 2

Square root of 3042 × 2 = 6084

Here

2 × 3 × 13 = 78

(v) 6300 = 2 × 2 × 3 × 3 × 5 × 5 × 7

We know that

6300/2 = 3150/2 = 1575/3 = 525/3 = 175/5 = 35/5 = 7/7 = 1

By pairing the same kind of factors, one factor 7 is left unpaired

So to make it a pair we must multiply it by 7

Required least number = 7

Square root of 6300 × 7 = 44100

Here

2 × 3 × 5 × 7 = 210

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