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Square root of 324

The square root of 324 is a number which, when multiplied by itself, results in 324. The number 324 is special because it is a perfect square root. This indicates that its square root is a whole number. We will now look at how to find the value of the square root of 324 and solve some problems to understand this concept better.

Square Root of 324: √324 = 18
Square 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, results in the original number. In the case of 324, the number 18 when multiplied by itself results in the number 324, making 18 a perfect square. However, you can also have square roots of some numbers that do not result in whole numbers, such as 5. We can express the square root of 324 in different ways.

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

Square root of 324

Is the Square Root of 324 Rational or Irrational?

  • The decimal part of the square root of 324 is terminating as it is 18.0; it also can be expressed as the ratio p/q, 18/1, which tells us that it is a rational number.
  • Therefore, we can conclude that the square root of 324 is rational.

How to Find the Square Root of 324?

There are 2 main methods we use to find the Square Root of 324:

  • Repeated subtraction
  • Long division

Click here to learn about other methods to find the square root of a number.

Repeated Subtraction

Start from 324 and keep subtracting successive odd numbers till we obtain zero. The total numbers we subtract is the square root of 324.

  1. 324 - 1 = 323
  2. 323 - 3 = 320
  3. 320 - 5 = 315
  4. 315 - 7 = 308
  5. 308 - 9 = 299
  6. 299 - 11 = 288
  7. 288 - 13 = 275
  8. 275 - 15 = 260
  9. 260 - 17 = 243
  10. 243 - 19 = 224
  11. 224 - 21 = 203
  12. 203 - 23 = 180
  13. 180 - 25 = 155
  14. 155 - 27 = 128
  15. 128 - 29 = 99
  16. 99 - 31 = 68
  17. 68 - 33 = 35
  18. 35 - 35 = 0

Since 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 24.
  • Step 2: Find a number such that when you multiply it with itself, the product is less than or equal to 03. We know that 12 = 1 which is less than 3. Dividing 3 by 1 with quotient as 1, we get 2 as the remainder.
  • Step 3: Remember to drag down the next pair of numbers, which is 24, making the next dividend 224. Also, adding 1 by itself gives us 2 which becomes the starting digit of our next divisor.
  • Step 4: Now we have 2X as our new divisor. We need to find the value of X such that 2X × X gives us a value less than or equal to 224. 8 fills the value of X to give us 28 × 8 = 224, resulting in the remainder becoming 0.

So our long division now looks like this: 

Therefore, the square root of 324 is 18.

Explore square roots using illustrations and interactive examples

Challenging Questions

  • What is the square root of the sum of the digits of the root of 324?
  • Find by repeated subtraction the roots of:
    • 729
    • 961
 

Solved Examples

  1. Example 1: Kevin wants to buy a square plot which is 324 square feet in area. He wants to build a road along the length of the boundary. If the cost of adding tar per feet is 40 dollars, find the cost of adding tar along the entire perimeter of the plot.

    Solution:

    First, to calculate the cost of adding tar, we would need the perimeter of the land.

    To find the perimeter, we need to find the side length first.

    Side length is the square root of the area of the square.

    Therefore, side length here will be √324 = 18, and perimeter 4 times this.

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

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

    Solution:

    We need to use the formula Time = Distance/Speed
    Speed = √324 = 18 mi/hr
    Distance = 9 miles
    Using the formula, Time = 9 / 18 = 0.5 hrs or 30 mins

    Therefore, 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. Therefore, it is a perfect square root.

What is the square of 324?

The square of 324 is 3242 = 104976

What is the square root of 324 simplified?

If you factor 324, you will find that 324 = 2 × 2 × 9 × 9, or 18 × 18. Therefore, the simplified form can be written as 182

Is the square root of 324 a rational number?

The square root of 324 is a rational number as it can be shown in the form p/q (18/1) and it has a terminating decimal place.

What is the exponent form of root 324?

The exponent form is 3241/2.

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