For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square. Also find the square root of the square number so obtained.
(a) 1620 ;(b) 9408 ;(c) 5292 ;(d) 9408 ;
(e) 1500
Answers
Answer:i) 252=
2×2
×
3×3
×7
Therefore, we need to divide 252 by 7 in order to make it a perfect square.
So,
7
252
=36
∴
36
=6
ii) 2925=
3×3
×
5×5
×13
Therefore, we need to divide 2925 by 13 in order to make it a perfect square.
So,
13
2925
=225
∴
225
=15
iii) 396=
2×2
×
3×3
×11
Therefore, we need to divide 396 by 11 in order to make it a perfect square.
So,
11
396
=36
∴
36
=6
iv) 2645=
23×23
×5
Therefore, we need to divide 2645 by 5 in order to make it a perfect square.
So,
5
2645
=529
∴
529
=23
v) 2800=
2×2
×
2×2
×
5×5
×7
Therefore, we need to divide 2800 by 7 in order to make it a perfect square.
So,
7
2800
=400
∴
400
=20
vi) 1620=
2×2
×
3×3
×
3×3
×5
Therefore, we need to divide 1620 by 5 in order to make it a perfect square.
So,
5
1620
=324
∴
324
=18
Answer:
Ncert solutions
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Mathematics
Science
Chapters in NCERT Solutions - Mathematics , Class 8
Exercises in Squares and Square Roots
Question 12
Q6) For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square. Also, find the square root of the square number so obtained:
(i) 252
(ii) 2925
(iii) 396
(iv) 2645
(v) 2800
(vi) 1620
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 divided by 7 to make it a perfect square.
\therefore252\div7=36∴252÷7=36
And \sqrt{36}=2\times3=6
36
=2×3=6
(ii) 2925 = 3 x 3 x 5 x 5 x 13
Here, prime factor 13 has no pair. Therefore 2925 must be divided by 13 to make it a perfect square.
\therefore2925\div13=225∴2925÷13=225
And \sqrt{225}=3\times5=15
225
=3×5=15
(iii) 396 = 2 x 2 x 3 x 3 x 11
Here, prime factor 11 has no pair. Therefore 396 must be divided by 11 to make it a perfect square.
\therefore396\div11=36∴396÷11=36
And \sqrt{36}=2\times3=6
36
=2×3=6
(iv) 2645 = 5 x 23 x 23
Here, prime factor 5 has no pair. Therefore 2645 must be divided by 5 to make it a perfect square.
\therefore2645\div5=529∴2645÷5=529
And \sqrt{529}=23
529
=23
(v) 2800 = 2 x 2 x 2 x 2 x 5 x 5 x 7
Here, prime factor 7 has no pair. Therefore 2800 must be divided by 7 to make it a perfect square.
\therefore2800\div7=400∴2800÷7=400
And \sqrt{400}=2\times2\times5=20
400
=2×2×5=20
(vi) 1620 = 2 x 2 x 3 x 3 x 3 x 3 x 5
Here, prime factor 5 has no pair. Therefore 1620 must be divided by 5 to make it a perfect square.
\therefore1620\div5=324∴1620÷5=324
And \sqrt{324}=2\times3\times3=18
324
=2×3×3=18