Find whether 1156 and 2800 are perfect squares using prime factor… - Vidyadip

Question

Find whether 1156 and 2800 are perfect squares using prime factorisation.

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Answer

(i) $1156=(2 \times 2) \times(17 \times 17)$
$\begin{array}{l}=2^2 \times 17^2 \\ =(2 \times 17)^2 \\ =(34)^2 \\ \therefore \sqrt{ } 1156=34\end{array}$
(ii) $2800=(2 \times 2) \times(2 \times 2) \times(5 \times 5) \times 7$
$=2^2 \times 2^2 \times 5^2 \times 7$
Since the factors cannot be paired
$\therefore 2800$ is not a perfect square.

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