Find the least number that must be added to the following to get a perfect square in each case:

a. 3451

b. 7896

c. 54,723

d. 18,355

e. 23,455

To find the least number that must be added to each given number to make it a perfect square, we will first identify the smallest integer whose square is larger than or equal to the number. Let's go through each case step by step:
a. 3451

Find the square root of 3451: 3451 ​ ≈ 58.73

The next whole number is 59.

Square 59 to find the nearest perfect square: 5 9 2 = 3481

Calculate the difference: 3481 − 3451 = 30


So, 30 must be added to 3451 to make it a perfect square.
b. 7896

Find the square root of 7896: 7896 ​ ≈ 88.82

The next whole number is 89.

Square 89: 8 9 2 = 7921

Calculate the difference: 7921 − 7896 = 25


So, 25 must be added to 7896 to make it a perfect square.
c. 54,723

Find the square root of 54723: 54723 ​ ≈ 233.85

The next whole number is 234.

Square 234: 23 4 2 = 54756

Calculate the difference: 54756 − 54723 = 33


So, 33 must be added to 54,723 to make it a perfect square.
d. 18,355

Find the square root of 18355: 18355 ​ ≈ 135.47

The next whole number is 136.

Square 136: 13 6 2 = 18496

Calculate the difference: 18496 − 18355 = 141


So, 141 must be added to 18,355 to make it a perfect square.
e. 23,455

Find the square root of 23455: 23455 ​ ≈ 153.19

The next whole number is 154.

Square 154: 15 4 2 = 23716

Calculate the difference: 23716 − 23455 = 261


So, 261 must be added to 23,455 to make it a perfect square.
In summary, the least numbers needed to be added are 30 , 25 , 33 , 141 , and 261 for each of the cases respectively.

Answered by OliviaLunaGracy | 2025-07-21

To convert the numbers into perfect squares, add 30 to 3451, 25 to 7896, 33 to 54,723, 141 to 18,355, and 261 to 23,455. This ensures each resulting number is a perfect square. Each addition is calculated by finding the nearest whole number square root and determining the difference from the next perfect square.
;

Answered by OliviaLunaGracy | 2025-07-31