Question

By what least number should 4851 be divided to get a perfect square number ? Also find the square root of the square number so obtained ?​

Answer 1

Answer:

11 is the least number and the when you take the square root of the number you get 21

Step-by-step explanation:

The easiest way to solve this problem is guess and check.

First of all, a perfect square NEEDS to be a WHOLE number

Since 4851 is odd, you cannot divide it by an even number evenly, as it would result in a number with a remainder or leftover decimal amount.

This means you cannot divide by 2, 4,8...etc

We just have to guess and check odd numbers starting at 3.

4581/ 3 = 1527                 sqrt(1527) = 39.07684737    decimal so not this one

4581/ 5 = 916.2               decimal so not this one

4581/ 7 = 654.4285714  decimal so not this one

4581/ 9 = 509                 sqrt(509) = 22.56102835     decimal so not this one

4581/ 11 = 441                  sqrt(441) = 21

This is the first instance where 4581 is divisible by a number that yields a perfect square, so 11 is the least number and the square root of the result is 21.

Answer 2

Answer:

The least number should 4851 be divided to get a perfect square number = 11

The square root of the obtained perfect square number is 21

Step-by-step explanation:

Given number = 4851

It can be written as

4851 = 3×1617

4851 = 3×3×539

4851 = 3×3×7×77

4851 = 3×3×7×7×11

4851 = (3×3)×(7×7)×11

It is clear that We should divide the given number by 11 then we get a perfect square number.

4851/11 = 441

441 = 21×21

=> 441 = 21²

=> √441 = √(21²)

=> √441 = 21

Answer:-

The least number should 4851 be divided to get a perfect square number = 11

The square root of the obtained perfect square number is 21

Used Method :-

→ Prime Factorization Method