Question

Q4: Find the smallest number by which 19602 must be divided, so that the
quotient is a perfect
square.

Answer 1

$Resolving \: 19602 \: into \:prime \: factors ,$

$we \: get$

2 | 19602

___________

3 | 9801

___________

3 | 3267

___________

3 | 1089

___________

3 | 363

___________

11| 121

___________

**** 11

19602 = 2 × 3 × 3 × 3 × 3 × 11 × 11

We can see that, 3, 3 and 11 exists in pairs while 2 is alone .

So, we must divide the given number by 2 .

Therefore.,

Perfect square obtained = 19602 ÷ 2 = 9801

Now , 9801 = 3×3 × 3 × 3 × 11 × 11

$\red{ Required \: perfect \: square }$

$= ( 3 \times 3 \times 11 )^{2}$

$\green { = 99^{2}}$

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