Answer :
Step-by-step explanation:
To find the smallest number that must be subtracted from 402 to make it a perfect square, we need to identify the largest perfect square less than or equal to 402 and then find the difference between 402 and that perfect square.
First, let's find the integer part of the square root of 402:
402
20.0499
402
The largest integer less than or equal to 20.0499 is 20.
Next, we square 20 to get the largest perfect square less than or equal to 402:
202=400
Now, we subtract this perfect square from 402:
402−400=2
So, the smallest number that must be subtracted from 402 to make it a perfect square is 2, and the resulting perfect square is 400. The square root of 400 is 20.
Therefore, we have:
The number to be subtracted: 2
The resulting perfect square: 400
The square root of the perfect square: 20