For the following number, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square numbers so obtained.
$180$

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Solution

Given number = 180
By prime factorization
$180 = 2 \times 2 \times 3 \times 3 \times 5$
In given factor '5' does not have any pair if '180' is multiplied By '5' then it will become perfect square.
$180 \times 5 = 900$
and $\sqrt{900} = 2 \times 3 \times 5 = 30$
square root of 900 is 30

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Question 5 (ii)

For the following number, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also, find the square root of the square number so obtained:

180

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For the following number, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square numbers so obtained. 180

Given number = 180By prime factorization180=2×2×3×3×5In given factor '5' does not have any pair if '180' is multiplied By '5' then it will become perfect square.180×5=900and √900=2×3×5=30square root of 900 is 30

For the following number, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square numbers so obtained.
$180$

Given number = 180
By prime factorization
$180 = 2 \times 2 \times 3 \times 3 \times 5$
In given factor '5' does not have any pair if '180' is multiplied By '5' then it will become perfect square.
$180 \times 5 = 900$
and $\sqrt{900} = 2 \times 3 \times 5 = 30$
square root of 900 is 30