Why is 14,400 a perfect square?

A perfect square is a number that can be expressed as the product of 2 equal rememberingsomer.com.

You are watching: What is the square root of 14400

The only method to accurately calculation if a number is a perfect square is to find the factors. Before we go v the trouble of finding the factors, over there is a fast trick you can use to assist determine if girlfriend need even need to execute the extra work.

Try these procedures first:

A number that is a perfect square never ever ends in 2, 3, 7 or 8. If your number ends in any type of of those numbers, you can stop here due to the fact that your number is no a perfect square. Achieve the digital source 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 action in an ext detail below. All possible numbers that are a perfect square have a digital source of 1, 4, 7, 9.

Let"s shot it...

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Step 1:

What is the last variety of 14,400? it is this number: 14400. The price is 0. Is 0 in the list of numbers that are never perfect squares (2, 3, 7 or 8)?

Answer: NO, 0 is not in the perform of numbers the are never perfect squares. Let"s continue to the following step.

Step 2:

We now need to obtain the digital root of the number. Here"s just how you perform it:

break-up the number up and add each number together:
1 + 4 + 4 + 0 + 0 = 9

What is the digital root of number 14,400?

Answer: 9

Step 3:

So currently we know the digital source of 14,400 is 9. Is 9 in the list of digital roots the are constantly a square root (1, 4, 7 or 9)?

Answer: YES, 9 is in the perform of digital roots the are always perfect squares. We have the right to conclude the 14,400 can be a perfect square!


OK, so currently we recognize that 14,400 might be a perfect square. We have actually to discover the components of the number to be sure.

Here are every one of the components of 14,400:

1 x 14,4002 x 7,2003 x 4,8004 x 3,6005 x 2,8806 x 2,4008 x 1,8009 x 1,60010 x 1,44012 x 1,20015 x 96016 x 90018 x 80020 x 72024 x 60025 x 57630 x 48032 x 45036 x 40040 x 36045 x 32048 x 30050 x 28860 x 24064 x 22572 x 20075 x 19280 x 18090 x 16096 x 150100 x 144120 x 120

Whoa! that is a most factors!

highlighted in orange over is the factor mix that makes 14,400 a perfect square. Perform you watch why? A number deserve to only be a perfect square if the product that two precisely the same numbers is equal to the initial number. Here"s the proof: 120 x 120 = 14,400

More Examples

Number 14,39814,39914,40114,402
Perfect Square? nononono