Question

Find the sq. root by prime factorization.
a) 11025 b) 8469 c) 17956

Answer 1

Answer:

a

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please

Answer 2

Answer:

• 11025 = (105)²
• 8469 = (3√941)²
• 17956 = (134)²

Step-by-step explanation:

a) 11025

$\Large{\begin{array}{c|c}\underline{5} & \underline{\;11025\;}\\\underline{5} & \underline{\;\;2205\;\;}\\\underline{3} &\underline{\;\;\;441\;\;\;}\\\underline{3}& \underline{\;\;\;147\;\;\;}\\\underline{7} & \underline{\;\;\;\;49\;\;\;\;}\\ \underline{7}&\underline{\;\;\;\;\;7\;\;\;\;\;}\\&{1}\end{array}}$

Hence,

11025 = (5 × 5 × 3 × 3 × 7 × 7)

= (5² × 3² × 7²) = (105)²

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b) 8469

$\Large{\begin{array}{c|c}\underline{3} & \underline{\;8469\;}\\\underline{3} & \underline{\;2843\;}\\&{\;\;\;941\;\;\;}\\\end{array}}$

Hence,

8469 = (3 × 3 × √941 × √941)

= (3² × √941²) = (3√941)²

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c) 17956

$\Large{\begin{array}{c|c}\underline{\;2\;} & \underline{\;17956\;}\\\underline{\;2\;} & \underline{\;\;8978\;\;}\\\underline{67} &\underline{\;\;4489\;\;}\\\underline{67}& \underline{\;\;\;\;67\:\;\;\;}\\& {1}\\ \end{array}}$

Hence,

17956 = (2 × 2 × 67 × 67)

= (2² × 67²) = (134)²