Question

using prime factorization method find which of the following are perfect square numbers: 1. 252 2. 324 3. 676 4. 1225 ( plzzzz with explanations​

Answer 1

2 and 4 are the perfect square of no 18 & 35 respectively

Answer 2

$1. Given \: number \: 252$

$Resolve \: 252\: into \: prime \:factors , we \:get$

2 | 252

________

2 | 126

________

3 | 63

________

3 | 21

________

****7

252 = 2 × 2 × 3 × 3 × 7

we see that 2,3 exist in pairs , while 7 is alone.

So, 252 is not a perfect square .

$2. Given \: number\: 324 .$

$Resolve \: 324 \: into \: Prime \: factors , \: we \:get$

2 | 324

_______

2 | 162

_______

3 | 81

_______

3 | 27

_______

3 | 9

_______

*** 3

324 = 2 × 2 × 3 × 3 × 3 × 3

We see that 2,3,3 exist in pairs .

$324 \: is \: a \: perfect \: square .$

$\red{ 324 } = ( 2 \times 3 \times 3 )^{2}$

$= 18^{2} \: \green { ( perfect \:square )}$

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