A: No, the number 123,456,789 is not a perfect square.

A perfect square is a number that can be expressed as the product of two equal integers.

The only way to accurately calculate if a number is a perfect square is to find the factors. Before we go through the trouble of finding the factors, there is a quick trick you can use to help determine if you need even need to do the extra work.

Try these steps first:

- A number that is a perfect square never ends in 2, 3, 7 or 8. If your number ends in any of those numbers, you can stop here because your number is not a perfect square.
- Obtain the digital root of the number. The digital root essentially is the sum of all of the digits. If you're lost, don't worry, we'll go over each step in more detail below.
- All possible numbers that are a perfect square have a digital root of 1, 4, 7, 9.

Let's try it...

**Step 1:**

What is the last number of 123,456,789? It is this number: 123456789. The answer is 9. Is 9 in the list of numbers that are never perfect squares (2, 3, 7 or 8)?

Answer: NO, 9 is not in the list of numbers that are never perfect squares. Let's continue to the next step.

**Step 2:**

We now need to obtain the digital root of the number. Here's how you do it:

- Split the number up and add each digit together:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45

If the answer is more than one digit, you would add each digit of the answer together again:

4 + 5 = 9

What is the digital root of number 123,456,789?

Answer: **9**

**Step 3:**

So now we know the digital root of 123,456,789 is
**9**. Is 9 in the list of digital roots that are always a square root (1, 4, 7 or 9)?

Answer: YES, 9 is in the list of digital roots that are always perfect squares. We can conclude that 123,456,789 could be a perfect square!

**Factoring**

OK, so now we know that 123,456,789 *could* be a perfect square. We have to find the factors of the number to be sure.

Here are all of the factors of 123,456,789:

1 x 123,456,7893 x 41,152,2639 x 13,717,4213,607 x 34,2273,803 x 32,46310,821 x 11,409

We're looking for a factor combination with equal numbers for X and Y (like 3x3) above. Notice there isn't a equal factor combination, that when multiplied together, produce the number 123,456,789. That means 123,456,789 is NOT a perfect square.

Number | 123,456,787 | 123,456,788 | 123,456,790 | 123,456,791 |

Perfect Square? | no | no | no | no |

General Questions

- How is the number 123,456,789 written in scientific notation?
- What is the absolute value of the number 123,456,789?
- What is the negative version of the number 123,456,789?
- What is the place value chart for the number 123,456,789?
- What is the digital root of the number 123,456,789?
- How many digits is in the number 123,456,789?

Factoring Questions

- What are the factors or divisors of the number 123,456,789?
- What are the prime factors of the number 123,456,789?
- What is the total number of factors of the number 123,456,789?
- What is the total number of prime factors of the number 123,456,789?
- What is the sum of all factors of the number 123,456,789 including 123,456,789?
- What is the sum of all factors of the number 123,456,789 excluding 123,456,789?
- What are the factor combinations of the number 123,456,789?
- What is the prime factorization of the number 123,456,789?

Calculation Questions

Miscellaneous Questions

- How much data will 123,456,789 bytes hold in different storage units?
- What is 123,456,789 in other base number systems?
- How is 123,456,789 spelled out in other languages or countries?
- How is 123,456,789 formatted in other languages or countries?
- How is 123,456,789 formatted as currency in different languages or countries?
- What are the different hash algorithm outputs for 123,456,789?