Question

find the square number by which 1800 must be multiplied so that it becomes a perfect square .also find the square root of the perfect square so obtained​

Answer 1

Answer:

60

Step-by-step explanation:

1800 = 18x100

= 3x6x2²x5²

= 2³x3²x5²

To become a perfect square it needs to be multiplied by 2 to make it's power even.

So,

2x1800 = 2⁴x3²x5²

Now, Square root is,

= √ (2⁴x3²x5²)

= 2²x3x5

= 60

So if we multiply 1800 by 2, we get a perfect square, 3600 whose root is 60.

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Answer 2

Answer:

Number by which 1800 must be multiplied to become a perfect square is 2 and , the square root of that number will be 60

Step-by-step explanation:

Find the prime factorisation of 1800 i.e.

1800 = 2 x 2 x 2 x 3 x 3 x 5

We find that in the above prime factorisation , 2 does not make a pair. If 2 gets a pair so the number will be a perfect square

1800 × 2 = 3600

3600 is a perfect square

Square root of 3600 is

$\sqrt{3600} =$ 60

Hope this helps you

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