Question

(1 STUU 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. (1) 252 (ii) 180 (iii) 1008 (iv) 2028 (v) 1458 (vi) 768 ​

Answer 1

Answer:

252 = 2 x 2 x 3 x 3 x 7

Here, prime factor 7 has no pair. Therefore 252 must be multiplied by 7 to make it a perfect square.

∴252×7=1764

And (i) √1764 =2×3×7=42

(ii) 180 = 2 x 2 x 3 x 3 x 5

Here, prime factor 5 has no pair. Therefore 180 must be multiplied by 5 to make it a perfect square.

∴180×5=900

And 900=2×3×5=30

(iii) 1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7

Here, prime factor 7 has no pair. Therefore 1008 must be multiplied by 7 to make it a perfect square.

∴1008×7=7056

7056=2×2×3×7=84

(iv) 2028 = 2 x 2 x 3 x 13 x 13

Here, prime factor 3 has no pair. Therefore 2028 must be multiplied by 3 to make it a perfect square.

∴2028×3=6084

6084 =2×2×3×3×13×13=78

(v) 1458 = 2 x 3 x 3 x 3 x 3 x 3 x 3

Here, prime factor 2 has no pair. Therefore 1458 must be multiplied by 2 to make it a perfect square.

∴1458×2=2916

2×3×3×3=54

2916 =2×3×3×3=54

(vi) 768 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3

Here, prime factor 3 has no pair. Tehrefore 768 must be multiplied by 3 to make it a perfect square.

∴768×3=2304

2304=2×2×2×2×3=48

I hope it helps you

Answer 2

Answer:

1.252

Step-by-step explanation:

2*2*3*3*7

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