The square root of 24 is a number which when multiplied by itself, results in the number 24. The value of a square root can be a decimal, whole number, and even a negative number. We will now look at how to calculate the square root of 24 and see a few interesting problems.

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**Square Root of 24: √24 = **4.8989...**Square of 24: 24² =** 576

1. | What is the Square Root of 24? |

2. | Is Square Root of 24 Rational or Irrational? |

3. | How to Find the Square Root of 24? |

4. | Important Notes |

5. | FAQs on Square Root of 24 |

## What is the Square Root of 24?

The square root of a number n is written as √n. It is the inverse operation of squaring a number just like multiplying is the inverse operation to dividing. The square root of 24 can be written in different ways

## Is Square Root of 24 Rational or Irrational?

Since the square root of 24 cannot be expressed as p/q, it is an irrational number.Long Division MethodPrime Factorization Method

One can find out more about the different methods by clicking here

### Long Division Method

The square root of 24 by long division method consists of the following steps:

**Step 1:**Starting from the left, first pair 24 and place a bar over the digits. We also pair the 0s in decimals in pairs of 2 from left to right.

**Step 3:**Drag a pair of 0’s down and fill it next to 8 to make the dividend 800.

**Step 4:**Double the divisor 4, and enter 8 below with a blank digit on its right. Guess the largest possible digit(X) to fill in the blank and the quotient for which the product of 8X and X results in a value less than or equal to 800. Divide and write the remainder.

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**Step 5:**Repeat this process to get the decimal places you want.

### Prime Factorization Method

The first step in this method is to find the prime factors of 24.24 = 2 × 2 × 2 × 3To find the root from here, we can simplify this to√24 = √(2 × 2 × 2 × 3)√24 = 2√6We can either leave it at this or find the root of 6 which is 2.45 and simplify further

Therefore, **Square Root of 24 = 2√6 ≅ 4.9**

**Explore Square roots using illustrations and interactive examples**

**Important Notes**

There are 2 real roots of 24, 4.899 and -4.899There will be n/2 digits in the square root of an even number with n digits.There will be (n+2)/2 digits in the square root of an odd number with n digits