Question

What will be the result, when the original number is multiplied with the square of the difference obtained in Q3? ​

Answer 1

Answer:

(i) 252=2×2×3×3×7

Here, 2 and 3 are in pairs but 7 needs a pair. Thus, 7 can become a pair after multiplying 252 with 7.

So, 252 will become a perfect square when multiplied by 7.

Thus, Answer = 7

perfect square no.= 252x7=1764

square root of 1764=42

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

Here, 3 and 2 are in pair but 5 needs a pair to make 180 a perfect square.

180 needs to be multiplied by 5 to become a perfect square.

Thus, Answer = 5

perfect square no.=180x5=900

square root of 900=30

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

Here, 2 and 3 are in pair, but 7 needs a pair to make 1008 a perfect square.

Thus, 1008 needs to be multiplied by 7 to become a perfect square

Hence, Answer = 7

perfect square no.=1008x7=7056

square root of 7056=84

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

Here, 2 and 13 are in pair, but 3 needs a pair to make 2028 a perfect square.

Thus, 2028 needs to be multiplied by 3 to become a perfect square.

Hence, Answer = 3

perfect square no.=2028x3=6084

square root of 6084=78

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

Here, 3 are in pair, but 2 needs a pair to make 1458 a perfect square.

So, 1458 needs to be multiplied by 2 to become a perfect square.

Therefore, Answer = 2

perfect square no.=1458x2=2916

square root of 2916=54

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

Here, 2 are in pair, but 3 needs a pair to make 768 a perfect square.

So, 768 needs to be multiplied by 3 to become a perfect square.

Hence, Answer = 3

perfect square no.= 768x3=2304

square root of 2304=48

Answer 2

Answer:

Here are two examples:

1. 1008 = 2x2x2x2x2, 3x3x3, and 7

Here, 2 and 3 are paired, but 7 lacks a pair to complete the square of 1008 as shown.

The result is that 1008 must be multiplied by 7 to form a perfect square

So, the answer is 7.

square number is 1008x7=7056.

7056 squared divided by 84

2. 2028 = 2 x 2 x 3 x 13 x 13 =

Here, 2 and 13 are paired, but 3 lacks a pair to complete the square of 2028.

In order for 2028 to be a perfect square, it must be multiplied by three.

So, the answer is 3.

2028x3=6084 is a perfect square number.

square of 6084 = 78

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