what is the least number that should be subtracted from 385 to get a perfect square? also find square root of the number
The correct answer and explanation is:
Correct Answer:
The least number that should be subtracted from 385 to get a perfect square is 1.
Perfect square obtained = 385 − 1 = 384
The nearest perfect square less than 385 is 384, but 384 is still not a perfect square.
We go further down to the next actual perfect square which is 361.
So, the least number that should be subtracted from 385 is 24.
Perfect square = 385 − 24 = 361
Square root of 361 = 19
Explanation (300 words):
To find the least number that must be subtracted from 385 to obtain a perfect square, one must look for the nearest perfect square less than 385. A perfect square is a number that can be expressed as the square of an integer.
Start by finding the square root of 385.
√385 ≈ 19.62 (This is not a whole number, so 385 is not a perfect square.)
Next, take the floor value of 19.62, which is 19.
Now, square this number: 19² = 361.
This means the largest perfect square less than 385 is 361.
To find how much we need to subtract from 385 to reach 361:
385 − 361 = 24
So, subtracting 24 from 385 gives 361, which is a perfect square.
Now, to find the square root of the resulting perfect square:
√361 = 19
Hence, the least number that should be subtracted from 385 to make it a perfect square is 24, and the square root of the resulting number is 19.
This method ensures that the subtraction gives the nearest lower perfect square. It is better to subtract the smallest amount possible to reach a perfect square rather than go for a higher one through addition. This is useful in number theory, estimating roots, and solving quantitative aptitude problems.