Math, asked by jishika0601, 1 month ago

find the largest no. of 3 digit which is a perfect square by prime factorisation method​

Answers

Answered by harinaa
1

Answer:

961

Step-by-step explanation:

999 - 38 = 961. Hence 961 isthe largest 3 digit perfect square whose square root is 31.

thank you

Answered by Vikramjeeth
6

*Question:-

find the largest no. of 3 digit which is a perfect square by prime factorisation method

*Answer:-

We know, the largest three-digit number is 999.

Also, our knowledge of elementary mathematics reminds us that:

(a + b)²= a² + 2 × a × b + b².

We know, 30² = 900; which is not very far from 999.

Putting a = 30 in the above equation, we get:

(30 + b)² = 30² + 2 × 30 × b + b²

Or, (30 + b)² = 900 + 60b + b²

Now, we have to check out for what largest integer value of b, the value of (60b + b²) remains less than or equal to 99.

Clearly b = 2 takes 60b to 120; so we can't take it.

For b = 1; (60b + b²) = 61 and this meets our requirement.

So, the largest three-digit number which is a perfect square is (30 + 1)² = 31² = 961.

hope \: it \: helps \: you

Hence,

961 is the answer.

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