Math Help. Non Calculator PLZZZ

This is the question. Show me how you got the answer, the methods and steps, and please dont use a calculator.

What is the smallest number that can be multiplied into 19800 to give a perfect square

For a number to be a perfect square, if we factorise it, all the factors MUST be arranged in pairs.
Example;
9=3x3
36=6x6 or 2x3x2x3 or (2x2)x(3x3)
225= 15x15= 3x5x3x5=(3x3)(5x5)

So, first factorise 19800.
19800= 5x5x2x3x3x2x2x11
19800=(5x5)(2x2)(3x3)(2)(11)

Here 2 and 11 are left without a pair.
So we have to multiply it with 2 and 11.
Or it is nothing but multiplying it with 22
So multiply 19800 with 22 to give a perfect square!
:D

Aww its ok.. best of luck!
Exam acche se likhna!

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I assume you mean "divided" into 19800.

Factor 19800: 2, 2, 2, 3, 3, 5, 5, 11

Look for number pairs. These form squares when multiplied out: 2, 2, 3, 3, 5, 5.

The remaining factors are 2, 11. The smallest number is 22.

19800 / 22 = 900. 900 is the perfect square.

19800 = 198 × 100 ----- here 100 is square number
= 2 × 99 × 100
= 2 × 11 × 9 × 100 -------- 100 and 9 are square numbers
so to get pair of 2 and 11 multiply by 2 and 11 i.e. 22
19800 × x = square number
x = 22
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