Question

by what smallest number must 180 be multiplied so that it becomes a prefect squares? also, find the square root of the number so obtained​

Answer 1

Answer:

Smallest number = 5

Square root = 30

Step-by-step explanation:

Factors of 180 = 2 × 2 × 3 × 3 × 5

Pairs are (2 × 2), (3 × 3). 5 doesn't have a pair

So we multiply 180 by 5 to get a pair

180 × 5 = 900

Factors of 900 = 2 × 2 × 3 × 3 × 5 × 5

So this is a perfect square

Now, square root of 900 is √(2 × 2 × 3 × 3 × 5 × 5)

= 2 × 3 × 5

= 30. ( 30 × 30 = 900)

Hope that helps

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Answer 2

Step-by-step explanation:

180=2^2*3^2*5

=(2*2)*(3*3)*5

To make the unpaired 5 into paired ,multiply the number with 5

therefore

180*5=2^2*3^*5^2

hence square root of number

=√180*√5

=2*3*5

=30