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Square Root of 104

The symbol for square root is written as √ and is an integral part of mathematics. Once you understand the basics of finding the square root of a number, you can solve any square root-related problem. In this short lesson, we will learn about the square root of 104. We will be using methods like prime factorization and division, learn how to find out the square root of 104, and look at some examples for a better understanding.

Square Root of 104: √104 = 10.198039027...
Square of 104: 1042 = 10816

1. What Is the Square Root of 104?
2. Is Square Root of 104 Rational or Irrational?
3. How to Find the Square Root of 104?
4. FAQs on Square Root of 104

What Is the Square Root of 104?

The square root of a number n is written as √n. This number when squared or multiplied by itself results in the original number n. The square root of 104 can be written in multiple ways.

  • Radical form: √104 = 2√26 
  • Decimal form: 10.198
  • Exponent form: (104)1/2

Is Square Root of 104 Rational or Irrational?

  • 104 is a number that is not a perfect square, meaning it does not have a natural number as its square root.
  • Also, its square root cannot be expressed as a fraction of the form p/q, which tells us that the square root of 104 is an irrational number.

How to Find the Square Root of 104?

There are multiple ways to find the square root of 104:

  • Long Division Method
  • Prime Factorization Method

One can find out more about these methods by clicking here.

Long Division Method

The square root of 104 by long division method consists of the following steps:

  • Step 1: Starting from the right, we will pair up the digits by putting a bar above 04 and 1 separately. We also pair the 0s in decimals in pairs of 2 from left to right.
  • Step 2: Find a number which, when multiplied by itself, gives a product less than or equal to 1. This will be 1 here, so place 1 in the quotient and the divisor's place, which will result in the remainder being 0. 
  • Step 3: Drag down 04 beside the remainder 0. Also, add the divisor to itself and write it below. (1+1=2)
  • Step 3:  Find a number X such that 2X × X results in a number less than or equal to 04. The number 0 fits here so fill it next to 2 in the divisor as well as next to 1 in the quotient. 
  • Step 4: Find the remainder and now drag down the pair of 0s from the decimal part of the number. Adding X to the divisor, the new divisor remains 20. 
  • Step 5: Repeat this process to get the decimal places you want.

Square Root of 104

Therefore, the square root of 104 = 10.198

Prime Factorization

  • To find the square root of 104, we shall first express it in terms of its prime factors.
    104 = 2 × 2 × 2 × 13
  • Next, this can be reduced further to
    104 = 23 × 13
  • Finally, to find the root of this from here is very easy:
    √104 = √(23 × 13)
    √104 = 2√26 = 10.198

Therefore, the square root of 104 = 10.198

Explore square roots using illustrations and interactive examples

Important Notes

  • There exists a positive and negative root of 104: 10.198 and -10.198.
  • The square root of 104 is an irrational number that is non-terminating.
  • There 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.

Challenging Questions

  • What is the square root of 104 up to 6 decimal places? (Use long division.)
  • Find the square root of the following numbers:
    • 10400
    • 0.104
 

Solved Examples

  1. Example 1: Jake wants to calculate the side length of the square garden at his home. It has an area of 104 square feet. Round your answer to the nearest whole number.

    Solution:

    To find the side of the garden, we will have to find the square root of 104. The square root is √104 = 10.198
    Hence, the side length of the garden is approximately 10 feet.

  2. Example 2: What will be the distance covered by a car travelling at √104 miles per hour in 2 hours?

    Solution:

    Distance covered = Speed × Time
    Therefore, the car covers a total distance of √104 × 2 = 10.198 × 2 = 20.396 miles

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FAQs on Square Root of 104

What is the prime factorization of 104?

Prime factorization of 104: 2 × 2 × 2 × 13

What is the square of 112?

The square of 112 is 112² = 12544

Is 104 a perfect square root?

104 is not a perfect square. 104 is a natural number, but since there is no other natural number that can be squared to result in the number 104, it is NOT a perfect square.

What is the decimal value of the square root of 104?

The decimal value of the square root of 104 is 10.198.

Is the square root of 104 a rational number?

No, the square root of 104 is not a rational number since the square root of 104 is non-terminating and cannot be represented in the form of p/q.

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