Question

5. Find the least square number which is exactly divisible by 6. Find the smallest number by which each of the following numbers should be multiplied so as perfect square. Also, find the square root of the perfect square thus obtained. (a) 3072 (b) 4802 (c) 1452 (d) 845 ​

Answer 1

Answer:

Solution:

(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