Question

Find the smallest whole number by which 180 should be multiplied so as to get perfect square number Also find the square root of the square number so obtained​

Answer 1

Hence, the smallest number by which 180 must be multiplied so that the product is a perfect square is 5. And the square root of the new number is √900=30. Here, 2 and 3 are in pair, but 7 needs a pair to make 1008 a perfect square. Thus, 1008 needs to be multiplied by 7 to become a perfect square.

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Answer 2

Answer:

The least number is 5 and the “square root” is 30.

Solution:

To find the “smallest number” by which 180 will be multiplied to get a “perfect square”, we need to factorize 180 as under:

180=2 \times 90180=2×90

=2 \times 9 \times 10=2×9×10

=2 \times 3 \times 3 \times 2 \times 5=2×3×3×2×5

=2^{2} \times 3^{2} \times 5=2

2

×3

2

×5

Now, 5 is not in square. If 5 is in square, then derived number will be perfect square.

Hence, 180 must be multiplied by 5 to get a “perfect square” as shown below:

180=2^{2} \times 3^{2} \times 5^{2}=4 \times 9 \times 25=900180=2

2

×3

2

×5

2

=4×9×25=900

Now, the square of 900 = 30

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