For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square:
I.1573
2.1323
please provide with proper answer pleaseee l have time limit please give a proper answer please!!!!
Answers
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