366 LearnersLast updated on May 26th, 2025
Square root of 104
A square root is a number when multiplied by itself gives the original number. The square of a number is represented as X² and the square root of a number is expressed as √x The square root of 104 is represented by √104 Square roots play a vital role in physics to determine the velocity of an object in free fall.
What Is the Square Root of 104?
The square root of 97 is approximately ±10.198
The square root of 104 is written as √104 in radical form. In exponential form, it is written as (104)1/2
Finding the Square Root of 104
We can find the square root of 104 through various methods. They are:
i) Prime factorization method
ii) Long division method
iii) Approximation/Estimation method
Square Root of 104 By Prime Factorization Method
To find the square root of 104 through the Prime Factorization method, there are various steps involved in the process:
Step 1: To find the square root of 104, first express it in its prime factors.
Here, 104 = 2×2×2×13
Step 2: Simplify the factors further
104 = 23 × 13
Step 3: Apply root on both sides
√104 = √(2×13)
√104 = 2√26
2√26 = 10.198
Therefore, the square root of √104 = 10.198
Square Root of 104 By Long division
Finding a square root of 104 by long division method consists of the following steps:
Step 1: Pair the digits by putting a bar above. Starting from the right, we will pair 04 and 1 separately. We will also pair the zeros in decimals in pairs of 2 from left to right.
Step 2: Find a number, when multiplied by itself, gives a product less than or equal to 1. Here it's 1, so place 1 in the quotient and the divisor place will result in the remainder 0.
Step 3: Bring down 4 beside the remainder 0, add the divisor to itself and write it below. 1+1=2
Step 4: Find the remainder and bring 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 the process to get the decimal places you want
Therefore, the √104 = 10.198
Square Root of 104 By Approximation
Steps to find the square root of 104 by approximation method are:
Step 1: First identify the perfect squares around 104.
We know that
102 = 100
112 = 121
So √104 is between 10 and 11.
Step 2: Since 104 is closer to 100 than 121, we can start by estimating a bit above 10. Let us go with 10.2
10.2×10.2 = 104.04, which is close to 104.
Step 3: To get a more precise value, we can continue with more decimal places
10.192 = 103.8361, it is slightly less than 104.
Step 4: Try 10.20
10.202 = 104.04, which is very close to 104.
Thus, the √104 is approximately 10.198
Common Mistakes and How to Avoid Them in the Square Root of 104
While finding the square root of 104, we often make some common mistakes, especially when we solve problems related to that. So, let’s see some common mistakes and their solutions
Mistake 1
Estimating square roots of non-perfect squares.
One might guess too high or too low while finding the square roots, try to estimate the value that is very close to the estimated square root.
Square Root of 104 Examples
Problem 1
Jimmy wants to calculate the side length of the square loan at his home. It has an area of 104 square feet.
√104 = 10.198
Hence the length of the loan is approx 10.198
Ans: 10.198
Explanation
To find the side length of the loan, we need to find the √104
Problem 2
What will be the distance covered by a train travelling at √104 miles per hour in 12 hours?
Distance covered = Speed x Time
√104×2 = 10.198×12 = 122.376 miles
Ans: 122.376 miles
Explanation
Apply the distance formula. Find the √104 and multiply it by 12 to get the desired distance.
Problem 3
Why is the square root of 104, not a whole number?
The square root of 104 is not a whole number because 104 is not a perfect square. A perfect square is a number that can be expressed as the product of two equal whole numbers.
Hence, √104 is not a whole number.
Explanation
For example, 25 is a perfect square because 5 × 5 = 25. However, 104 cannot be expressed as the product of two equal whole numbers, so its square root is not a whole number.
Problem 4
How can we find the exact value of the square root of 104?
The exact value of the square root of 104 cannot be expressed as a simple fraction or decimal. It is an irrational number.
We cannot find the exact value of √104
Explanation
Irrational numbers are numbers that cannot be expressed as a simple fraction. The square root of 104 is one such number.
While we can approximate its value using methods like estimation or calculators, there is no exact, finite decimal representation.
Problem 5
Can we find the square root of 104 using a calculator?
Yes, we can find the square root of 104 using a calculator. Most calculators have a square root function.
Explanation
Enter 104 into the calculator and then press the square root button. The calculator will display the approximate value of the square root.
FAQs on 53 Square Root
1.How do you simplify √104
2.What are the factors of 104?
3.How to solve √114?
4.How to solve √30?
5.Is 104 divisible by 7?
6.How does learning Algebra help students in Philippines make better decisions in daily life?
7.How can cultural or local activities in Philippines support learning Algebra topics such as Square root of 104?
8.How do technology and digital tools in Philippines support learning Algebra and Square root of 104?
9.Does learning Algebra support future career opportunities for students in Philippines?
Important Glossaries for Square Root of 104
- Velocity:It is a measure of how fast something is moving in a specific direction.
- Prime factors:Prime factors are the prime numbers that multiply together to give the original number.
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Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
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