find the largest no. of 3 digit which is a perfect square by prime factorisation method
Answers
Answer:
961
Step-by-step explanation:
999 - 38 = 961. Hence 961 isthe largest 3 digit perfect square whose square root is 31.
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*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.