Question

Question 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:
(iv) 2028 (v)1458​

Answer 1

Answer:

(i) 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.

\therefore252\times7=1764∴252×7=1764

And (i) \sqrt{1764}=2\times3\times7=42

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.

\therefore180\times5=900∴180×5=900

And \sqrt{900}=2\times3\times5=30

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.

\therefore1008\times7=7056∴1008×7=7056

And \sqrt{7056}=2\times2\times3\times7=84

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.

\therefore2028\times3=6084∴2028×3=6084

And \sqrt{6084}=2\times2\times3\times3\times13\times13=78

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.

\therefore1458\times2=2916∴1458×2=2916

And \sqrt{2916}=2\times3\times3\times3=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.

\therefore768\times3=2304∴768×3=2304

And \sqrt{2304}=2\times2\times2\times2\times3=48

2304

=2×2×2×2×3=48

Answer 2

(iv) 2028

:- 45.04

➖➖➖➖➖➖➖➖➖➖➖➖➖

(v)1458

:- 38.06

➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖