Question

3.
By what smallest number must 180 be multiplied so that it becomes a perfect
square? Also, find the square root of the number so obtained.
70​

Answer 1

the least number by 180 must be multiplied is = 5 180 = 2×2×3×3×5

180×5 = 900

and the square root of 900 is = 30

Answer 2

Answer :

• 30 is the square root of 90.

Given :

• Smallest number must be 180 to be multiplied

To find :

• By what smallest number must 180 be multiplied so that it becomes a perfect square
• Square root of number so obtained

Solution :

First we have to find the prime factorization of 180 :

》180 = 2 × 3 × 3 × 2 × 5

2 and 3 are pairs but 5 is not pair. so we have to multiply the number with 5 to become a perfect square

》5 × 180

》900

We have to find the square root of the number so obtained :

Now we have to find the prime factorization of 900 :

》900 = 3 × 3 × 2 × 2 × 5 × 5

》3 × 2 × 5

》30

Hence , 30 is the square root of 90.