To find square root of 180 , we first factor it out .
To find the factors of 180 , we make a tree diagram .
180 can be written in factor form as : -
180 = 2 * 2 * 3 * 3 * 5
Here 2 comes twice , 3 comes twice and 5 comes only once .
This can be rewritten as
180 = 2^2 ˣ 3^2 ˣ 5
Taking Square root both sides , we get
√(180 ) = √ ( 2^2 * 3^2 * 5)
[Power of 2 got cancelled with square root sign . Thus we left with 2 and 3 and square root 5 ]
This gives 2 * 3 * √ 5 = 6 √ 5
We know value of square root 5 is 2.236 .
Thus square root of 180 is 6 √5 = 6 * 2.236 = 13.4164 .