find the smallest number by which 12600 multiplied so that it becomes a perfect square also find the square root of the perfect square so obtained
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find the smallest number by which 12600 multiplied so that it becomes a perfect square also find the square root of the
right answer of this is= 7
Verified answer
Given:
Solution:
By Prime Factorisation method,
The prime factors 2, 3 and 5 are in pairs. But the prime factors 2 and 7 are not in pairs.
∴⠀⠀2 × 7 = 14 should be multiplied with 12600, so that it becomes a perfect square.
So, now, we need to find the square root of 176400.
By Prime Factorisation method,
[tex]\\ \sf \: \: \: \: \: \: \: 176400 = 2 \times 2 \: \times2 \times 2 \times 3\times 3 \times 5 \times 5 \times 7 \times 7\\ \\ \\ \sf \therefore \: \sqrt{176400} \: \: = { \sqrt{ \underline{2 \times 2} \times{ \underline{2 \times 2}} \times {\underline{3 \times3 }}\times { \underline{5 \times 5 } \times {\underline{7 \times7}}} }} \\ \\ \\ \sf = 2 \times2 \times 3 \times 5 \times 7\: \: \: \: \: \: \: \: \: \\ \\ \\ \sf = 420 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]
[tex]\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: { \purple { \pmb{ \underline{Hence, \: The \: square \: root \: of \: 176400 \: = \: 420 \: }}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]
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