0
- Find the square root of 999;
- Remove the fractional (decimal) part to leave a whole number; and
- Square it.
A perfect square number is made by squaring an integer. The largest three digit perfect square number will be a little bit greater than 302 = 900. So it will be (3A)2. Using the formula for the square of a binomial, a2 + 2ab + b2, A = 1. Thus, (30 +1)2 = 302 + 2(30)(1) + 12 = 961 is the largest perfect square number.
Check 32:
322 = (30 + 2)2 = 900 + 2(30)(2) + 22 = 900 + 120 + 4 = 1024 (4-digits)
You can work faster like this:
312 = 3212; 901 + 2(3)(1)(10) = 961
322 = 3222; 904 + 2(3)(2)(10) = 1024
562 = 5262; 2536 + 600 = 3136
Still curious? Ask our experts.
Chat with our AI personalities
Coach
Vivi
JudyAdd your answer:
Earn +20 pts
Which is the largest 4 digit number which is a perfect square?
10000 is the square of 100 so you're looking for the square of 99 which is 9801.
How is 100 a perfect square?
It is the square of an integer: that is what a perfect square is.
How do you make 5 digit numbers as square?
The smallest 5 digit number is 10000 = 1002 The largest 5 digit number is 99999 and 3162 < 99999 < 3172 So, take any number between 100 and 316 (both inclusive) and square it to get a 5-digit perfect square.
Is the three-digit number X64 a perfect square?
x64 is not a perfect square any number if it is a 3-digit perfect square and ending with 4 it can be 144,324 ,484 and 784 because the number is ending with 4 but the tens digit is not matching to any of the option so it is not a perfect square
What is the largest three-digit perfect cube?
729
