What are referred to as perfect square or square number?

Natural numbers that room squares of other natural numbers are called perfect square or square number. because that example; We know that; 1 = 1²; 4 = 2²; 9 = 3²; 16 = 4²; 25 = 5² and also so on. Thus 1, 4, 9, 16, 25, etc., space perfect squares.

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To uncover out if the given number is a perfect square:If the prime factors of a number room grouped in bag of same factors, then that number is dubbed a perfect square. Or, in other words if a perfect square number is always expressible together the product of pairs of equal factors.


1. Find out if the complying with numbers are perfect squares:     (i) 144     (ii) 90     (iii) 180 (i) 144Resolving 144 into prime factors, we get


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144 = 2 × 2 × 2 × 2 × 3 × 3 (grouping the factors into the pairs of same factors) Therefore, 144 is a perfect square.

(ii) 90Resolving 90 right into prime factors, us get


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90 = 2 × 3 × 3 × 5(Here 3 is group in pairs of same factors and also 2 and also 5 are not group in pairs of equal factors) Therefore, 90 is no a perfect square.

(iii) 180 addressing 180 into prime factors, we get


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180 = 2 × 2 × 3 × 3 × 5(Here 2 and 3 room grouped in bag of same factors and also 5 is no grouped in pairs of same factors) Therefore, 180 is not a perfect square.

2. Is 36 a perfect square? If so, discover the number whose square is 36.

Solution:Resolving 36 into prime factors, we get


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36 = 2 × 2 × 3 × 3.Thus, 36 can be expressed as a product of pairs of equal factors.Therefore, 36 is a perfect square. Also, 36 = (2 × 3) × (2 × 3) = (6 × 6) = 6²Hence, 6 is the number who square is 36.

3. Is 196 a perfect square? If so, uncover the number who square is 196. Solution: addressing 196 into prime factors, we gain


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196 = 2 x 2 x 7 x 7. Thus, 196 deserve to be expressed as a product of pairs of equal factors. Therefore, 196 is a perfect square. Also, 196 = (2 x 7) x (2 x 7) = (14 x 14) = (14)². Hence, 14 is the number who square is 196.

4. Show that 200 is not a perfect square. Solution: solving 200 right into prime factors, we get


200 =2 x 2 x 2 x 5 x 5. Making bag of equal factors, we find that 2 is left. Hence, 200 is no a perfect square.

5. Uncover the smallest number whereby 252 have to be multiply to make it a perfect square. Solution: 252 = 2 × 2 × 3 × 3 × 7We observe the 2 and also 3 room grouped in pairs and 7 is left unpaired. If we multiply 252 by the factor 7 then, 252 × 7 = 2 × 2 × 3 × 3 × 7 × 71764 = 2 × 2 × 3 × 3 × 7 × 7, i beg your pardon is a perfect square. Therefore, the compelled smallest number is 7.

6. Discover the the smallest number whereby 396 have to be split so regarding get a perfect square. Solution: 396 = 2 × 2 × 3 × 3 × 11We observe that 2 and 3 space grouped in pairs and also 11 is left unpaired. If we divide 396 by the factor 11 then, 396 ÷ 11 = (2 × 2 × 3 × 3 × 1̶1̶)/1̶1̶= 2 × 2 × 3 × 3 = 36, i m sorry is a perfect square. Therefore, the compelled smallest number is 11.

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