find the smallest number by which the following numbers should be multiplied to get a perfect square number also find the square root of the square number so obtained :
Answers
Ncert solutions
Grade 8
Mathematics
Science
Chapters in NCERT Solutions - Mathematics , Class 8
Exercises in Squares and Square Roots
Question 5
Q5) 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
Solution
Transcript
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