Question
Using the prime factorisation method, find the following numbers are perfect squares:
$11025$
$11025$
✓
Answer
A perfect square can always be expressed as a product of equal factors.
Resolving into prime factors:
$11025$
$= 441 \times 25$
$= 49 \times 9 \times 5 \times 5$
$= 7 \times 7 \times 3 \times 3 \times 5 \times 5$
$= 7 \times 5 \times 3 \times 7 \times 5 \times 3$
$= 105 \times 105$
$= (105)^2$
Thus, $11025$ is a perfect square.
Resolving into prime factors:
$11025$
$= 441 \times 25$
$= 49 \times 9 \times 5 \times 5$
$= 7 \times 7 \times 3 \times 3 \times 5 \times 5$
$= 7 \times 5 \times 3 \times 7 \times 5 \times 3$
$= 105 \times 105$
$= (105)^2$
Thus, $11025$ is a perfect square.
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