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What least natural number must be added to 6072 to make it a perfect square?
12
16
6
10
12
Find the square root of 6072 using estimation; 772=5929 and 782=6084. The difference between 782 and 6072 is the required number.
We are given the number 6072.
x2=n+k
Find the square root of 6072 using estimation; 772=5929 and 782=6084. The difference between 782 and 6072 is the required number.
Many students subtract to find the number to be subtracted (6072 - 5929 = 143) instead of adding to reach the next perfect square.
Estimate the square root
We check squares near 6072. We know 702=4900 and 802=6400.
772=5929,782=6084
Identify the next perfect square
Since 6072 is between 772 and 782, the next perfect square is 782=6084.
782=6084
Calculate the difference
Subtract the given number from the next perfect square to find the value to add.
6084тИТ6072=12
A is correct because 12 must be added to 6072 to result in 6084, which is the perfect square of 78.
This technique is standard for questions asking for the 'least number to be added/subtracted' to make a number a perfect square or perfect cube.
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