Question

3. Find the least number by which each of th
given numbers should be multiplied so as to ge
a perfect square. Also, find the square root of th
resulting number 1260,252,117,1452​

Answer 1

Answer:

8th

Maths

Squares and Square Roots

Square Roots

For each of the following n...

MATHS

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

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ANSWER

(i) 252 = 2 x 2 x 3 x 3 x 7

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

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

Thus, Answer = 7

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

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

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

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

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

square no.= 768x3=2304

square root of 2304=48

Answer 2

Answer:

Step-by-step explanation:

ANSWER

(i) 252 = 2 x 2 x 3 x 3 x 7

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

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

Thus, Answer = 7

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

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

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

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

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

square no.= 768x3=2304

square root of 2304=48