find the smallest number by which each of the given numbers must be divided so that the quotient is perfect square also find the square root of this qoutient. (i) 2700 (ii) 5488 (iii)7203 (iv) 20886
Answers
Step-by-step explanation:
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
=2×2×2×2×3=48
Answer:
(i)2700 3
(ii)5488 7
(iii)7203 3
(iv)20886 2