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Questions  >>  Olympiad-Math  >>  Class 8
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Q)

Find the smallest number by which 252 must be mutiplied to make it a perfect square.

$\begin{array}{1 1} 6 \\ 7 \\ 8\\9 \end{array} $

4 Answers

Comment
A)
Solution :
$252 = 2\times 2 \times 3 \times 3 \times 7$
We observe that 2 and 3 are grouped in pairs and the 7 is left un paired.
If we multiply $252$ by the factor 7 then
$252 \times 7 = 2 \times 2 \times 3 \times 3 \times7 \times 7$
$1764 = 2 \times \times \times 3 \times 3 \times 7 \times 7$
Which is a perfect square.
$\therefore$ required number is 7
Answer:7
 
Comment
A)
Option (b) 7 because if we multiply 252×7=1764 That is a perfect square. 1764 =2×2×3×3×7×7 Therefore if we multiply 252×7= we get perfect square
 
Comment
A)
Solution : 252=2×2×3×3×7 We observe that 2 and 3 are grouped in pairs and the 7 is left un paired. If we multiply 252 by the factor 7 then 252×7=2×2×3×3×7×7 1764=2×××3×3×7×7 Which is a perfect square. ∴ required number is 7 Answer:7
 
Comment
A)
2*2*3*3*7. 7pair in incomplete so, we take 7 ans= 7
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