Question

# Find the square root of $1089$ using prime factorization.

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Solution

## Finding the square root using prime factorizationGiven number $1089$A perfect square can always be expressed as a product of pairs of equal factors.So, $1089=3×3×11×11={3}^{2}×{11}^{2}$Hence, square root of $1089=\sqrt{{3}^{2}×{11}^{2}}=3×11=33$ .

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