Question

find the smallest square root which is divided by 4 9 and 10​

Answer 1

smallest square root which is divided by 4 9 and 10 is 900.

Answer 2

Answer:

$\huge\tt\underline{question}$

Find the smallest square root which is divided by 4,9 and 10

$\huge\tt\underline{given}$

given numbers= 4,9 and 10

$\huge\tt\underline{to\:find}$

smallest square root which can be divided by 4,9 and 10

$\huge\tt\underline{solution}$

find the factors of the following numbers:

2| 4,9,10

2| 2,9,5

3|1,9,5

3|1,3,5

5|1,1,5

⠀|1,1,1

hence,the factors of each number are:

4 = 2×2

9 = 3×3

10 = 2×5

so,the LCM of the three numbers will be:

LCM(4,9,10) = 2×2×3×3×5 =180

hence,the LCM of the three numbers is 180

where 180 is not a perfect number.

to make a perfect square,all the factors of the number should be in pairs; hence we can conclude when the factors is multiplied by 5,it will make a square number.

180 = 2×2 ×3×3 ×5

180×5 = 2×2×3×3×5×5 = 900

$\huge\tt\underline{answer}$

hence,900 is the smallest square number divisible by each number 4,9,10