The square root of 324 is a number which, when multiplied by itself, results in 324. The number 324 is one-of-a-kind because it is a perfect square root. This indicates that its square root is a entirety number. We will now look at just how to find the worth of the square root of 324 and also resolve some problems to understand this concept better.

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Square Root of 324: √324 = 18Square of 324: 3242 = 104976

1.What Is the Square Root of 324?
2.Is the Square Root of 324 Rational or Irrational?
3.How to Find the Square Root of 324?
4.FAQs on Square Root of 324

What Is the Square Root of 324?

The square root of a number is a number which, when multiplied by itself, outcomes in the original number. In the case of 324, the number 18 when multiplied by itself outcomes in the number 324, making 18 a perfect square. However, you deserve to also have actually square roots of some numbers that carry out not cause totality numbers, such as 5. We have the right to express the square root of 324 in various ways.


Decimal form: 18.0Radical form: √324Exponent form: (324)1/2

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Is the Square Root of 324 Rational or Irrational?

As such, we deserve to conclude that the square root of 324 is rational.

How to Find the Square Root of 324?

Tbelow are 2 major approaches we usage to uncover the Square Root of 324:


Repeated subtractionLong division

Click below to learn around other techniques to uncover the square root of a number.

Repeated Subtraction

Start from 324 and keep subtracting succeeding odd numbers till we acquire zero. The complete numbers we subtract is the square root of 324.

324 - 1 = 323323 - 3 = 320320 - 5 = 315315 - 7 = 308308 - 9 = 299299 - 11 = 288288 - 13 = 275275 - 15 = 260260 - 17 = 243243 - 19 = 224224 - 21 = 203203 - 23 = 180180 - 25 = 155155 - 27 = 128128 - 29 = 9999 - 31 = 6868 - 33 = 3535 - 35 = 0

Because the total numbers we subtract is 18, the square root of 324 is 18.

Long Division

Step 1: Place a bar over the digits 03 and also 24.Tip 3: Remember to drag dvery own the next pair of numbers, which is 24, making the next dividfinish 224. Also, adding 1 by itself provides us 2 which becomes the founding digit of our next divisor.

So our long department now looks prefer this: 

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As such, the square root of 324 is 18.

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Challenging Questions


What is the square root of the sum of the digits of the root of 324?Find by repetitive subtractivity the roots of:729961

Solved Examples


Example 1: Kevin desires to buy a square plot which is 324 square feet in area. He desires to build a road along the size of the boundary. If the cost of adding tar per feet is 40 dollars, uncover the expense of including tar alengthy the whole perimeter of the plot.


Solution:

First, to calculate the cost of including tar, we would certainly require the perimeter of the land also.

To uncover the perimeter, we must find the side length first.

Side size is the square root of the location of the square.

Thus, side size here will certainly be √324 = 18, and perimeter 4 times this.

Therefore, the full cost of adding tar = 4 × 18 × 40= $2880


Example 2: Chris is cycling to his office at a rate of √324 mi/hr. How much time will certainly he take if he has to cover a distance of 9 miles?

Solution:

We must usage the formula Time = Distance/SpeedSpeed = √324 = 18 mi/hrDistance = 9 milesUsing the formula, Time = 9 / 18 = 0.5 hrs or 30 mins

As such, Chris will take 30 mins to reach his office.


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FAQs on Square Root of 324

Is 324 a perfect square root?


The square root of 324 is √324 = 18. As such, it is a perfect square root.

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What is the square of 324?

The square of 324 is 3242 = 104976

What is the square root of 324 simplified?

If you element 324, you will certainly discover that 324 = 2 × 2 × 9 × 9, or 18 × 18. As such, the simplified form have the right to be written as 182

Is the square root of 324 a rational number?

The square root of 324 is a rational number as it deserve to be displayed in the develop p/q (18/1) and also it has actually a terminating decimal location.