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# Find the square roots of the following numbers by the Prime Factorisation Method.(i) 729 (ii) 400 (iii) 1764 (iv) 4096 (v) 7744 (vi) 9604 (vii) 5929 (viii) 9216 (ix) 529 (x) 8100

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Solution

## (i) 729 can be factorized as follows.3729324338132739331⇒729=3×3×3×3×3×3=32×32×32∴√729=3×3×3=27(ii) 400 can be factorized as follows.240022002100250525551⇒400=2×2×2×2×5×5=22×22×52∴√400=2×2×5=20(iii) 17264 can be factorized as follows.21764288234413147749771⇒17264=2×2×3×3×7×7=22×32×72∴√1764=2×3×7=42(iv) 4096 can be factorized as follows.2409622048210242512225621282642322162824221⇒4096=2×2×2×2×2×2×2×2×2×2×2×2=22×22×22×22×22×22∴√1764=2×2×2×2×2×2=64(v) 7744 can be factorized as follows.2774423872219362968248422421112111111⇒7744=2×2×2×2×2×2×11×11=22×22×22×112∴√1764=2×2×2×11=88(vi) 9604 can be factorized as follows.2960424802724017343749771⇒9604=2×2×7×7×7×7=22×72×72∴√9604=2×7×7=98(vii) 5929 can be factorized as follows.7592978471112111111⇒5929=7×7×11×11=72×112∴√5929=7×11=77(viii) 9216 can be factorized as follows.2921624608223042115225762288214427223621839331⇒9216=2×2×2×2×2×2×2×2×2×2×3×3=22×22×22×22×22×32∴√5929=2×2×2×2×2×3=96(ix) 529 can be factorized as follows.2352923231⇒529=23×23=232⇒√529=23(x) 8100 can be factorized as follows.28100240503202536753225375525551⇒8100=2×2×3×3×3×3×5×5=22×32×33×52∴√529=2×3×3×5=90  Suggest Corrections  19      Similar questions  Explore more