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Q.

Find the square-root of https://lh5.googleusercontent.com/nep4JWLad9o2bPtTv3lKdkyzVGWwY93_jWUHryVDqcbOQW0InTGpu3TYcrRMX8HNIf_LTiYcmb-EkERD3Y0x5IpjfRgLoT7hwvdVkne0P5a8CWFqTOKnf5rgflviVh5mbLPxKYfl1PYeo-6JJbN_VA


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a

https://lh4.googleusercontent.com/enhSGjs8_r0AwmlNkOPj5HH25d-Yg84tdlgDoit96mqkCHcZzvUccexX5GOLm7mA_X-UvRkLFG1sHuiHZCxp_vVjbHvVFiw0h6I-XOmZtRURztWLamP3BhADbe7KlhFBvESnTBz-cpG3IxHlwUxgpw

b

https://lh4.googleusercontent.com/hidCwxut8_Szr18_e9x8duolWFvTsnejVuEggMr_q17s3Fa5TiCATrvusx_8kqTc3wzDN7m_0Y6r2YzQbzzXAykytKn0UXO83xIJFau3eaEwfv-WIG5qyvq0zwVbM20IZe3ilhMMIOZvk4uJkPGLsQ

c

https://lh5.googleusercontent.com/zuW9yftSgfGabURfd7_X_m32kE13ovKHxkS6XE0lp2DB6ymsJ1N5Rn28FTDD8VvwIBgUcDrV-Lua9u-Q8zwdDmCnHEuLbvuA3JgL0vwnT917Frg-SvXETXHnRLGVZMGORHIRqy8fg1bzzs48yYY7Xg

d

https://lh6.googleusercontent.com/cZxhiIxFzb1m5BuFFLadAy_3AJCSCh08yk_AfNomGbyDU7Xp7hHuhLzMom7BE_h_gDVcfmd-0ZM0tAOOAY3s6mrQI_VkgI5dTlREz4Lt4ZcF2v9Iq9v_eLi4KcTtJTGKR8CePMIzG8XJinecUtnCCg

answer is C.

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Detailed Solution

Concept: When a number (A) is multiplied by itself, the result is the number's square-root (A) . One can use the prime factorization technique to determine the square root of one. Make pairs of the same factors by determining the number's prime factors. Each pair's factor should be written down and multiplied. This item is the necessary square-root.
We must first simplify the fraction to its simplest form.
In order to do this, we divide the numerator and denominator numbers into their prime factors.
We know that https://lh6.googleusercontent.com/pxNmj_V3FDagO9z8RhUjTDtQpmpOoIQs5Gkn9fWwrAkGlIgpG3Rg9HyuNR4qOak6AH_QWsrS4zTfbBU2lKs4QllclNrow1h3b9kMk7XqP8zPTnOl8CeKzaHs4fy0SWo99f7X2wssHGSCc22b3F5HsQ and https://lh4.googleusercontent.com/l66REpk4Yqm882VcTqYaeBNi7d2uEkTF4aAgkYutKrkw67C-lOtMPxWbdq2mWfoSwDOwXH1lYy3la70P1kqJ9pf5vAs5yjq6aZTLJDYMbcp_2Bb3ZvX-OzzssNhZVH3uuuRQT2jbWTpE0pOqVLm9wA so we can write-
https://lh4.googleusercontent.com/8TsCts4Oo_lt-m2nsdRPzG0Jl9dl2mo8ZqgAgNkCHKZqdYVD2c9ufErNg9Gsn8jWiJcB0JVBmjWQHUtzYevvn5NtT3kjPei15SQFS_wplT_AmuTrzK4p4KmP9dl42BplCNMdnn46703_lc-iqPzhHAMake the pair of related factors so that they are both the same and have the same number.
In this case, we can see that https://lh3.googleusercontent.com/ZoNzZxgxhuhn7JeullvbaCB77Z8bTZkV9-MgDyx2HVLbGxCwqmWCisnK8byg3nfYqFm5gOL7tiutX5lrUD6q1PgPbaggN6NSz_6xIru-A3X2qA-6i8B0aIEFp3-VvLNBku2BxmmUoZEy5zL5p0nQfw and https://lh5.googleusercontent.com/FAiWWEu6DWMrYxSplLU0Lj_Fcr7ooxYzYRnHE1hTtNGwAwPUxr58msjnQlAN55aCOK93D1rLwMrt-cYgpaJIanLzfzanlAiWGnlZ_Womr6RRAnBVHSnEQZiAOKn0ni-vMGRbZUXIpEE89ATeEwg7ygare two pairs in the numerator with both factors being equal in the pairs.
And a pair of these equal factors https://lh3.googleusercontent.com/E6D-9I-ihqWMC8GcGi-OoKKL5S-FoZ2GW3dzXUA9XslnVgAtMpDwOUavcscfaa8HOAvyEbrBbNT6sMV-VzhP3v7IOZ5gU9SjcIKKJ8Mu9ld7LBBHMTsJvgIYcaTJ8nN6zjshri50NQMzRwVMYER8pware included in the denominator as well.
So we can write-
https://lh5.googleusercontent.com/qD8PxCgXzI6MnugMpRvKFgWn3teupVeSIlonrOEahG9-9hXcBUDohcGQf27hKjJ0kW8g0VKYdRa-dLAsjvP8cDibO2ZMbtowpAcBOiXP494XrYeagCPjXR8f-rN_kqdw0Lsi-mpS2ndzfse-arE-KwAfterward, subtract a factor from each pair from the square-root.
https://lh6.googleusercontent.com/kqe908DeT4-7aTBwWbqcusK4qMgqKtsaIEmcNeltUdAAqjdIVcOww0DkhsBVMEYhox9NgKMIn18lcF_TnhNp07ghqmqzN--7bk3DWqdG4b_S74UOyc9FAgaoUMzxqFjtAAKGFLQqnR6z-rGaosyyyQFinding the product of the factors derived from each pair of factors by multiplying the factors. The square-root of the provided fraction is this product.
https://lh4.googleusercontent.com/7cKsAcXYDEP3Gn4uJF2v2hW1IxyrhFMviom8LdfCzcNA7FQNJKX6al0prTzs4aRPrpEuzSqfAWvic3D0gwhapisbKYqh80dzKnezmQgJFFXOiegITQ2zSixHA1VnFwxWAml-zUjmcdCTNQJ94r6hLgHence, the correct answer is option 3) https://lh5.googleusercontent.com/zuW9yftSgfGabURfd7_X_m32kE13ovKHxkS6XE0lp2DB6ymsJ1N5Rn28FTDD8VvwIBgUcDrV-Lua9u-Q8zwdDmCnHEuLbvuA3JgL0vwnT917Frg-SvXETXHnRLGVZMGORHIRqy8fg1bzzs48yYY7Xg 
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