284 LearnersLast updated on May 26th, 2025
Square root of 84.
When someone asks you to explain a square root, you can just tell that it is a number when multiplied by itself produces the same number. As we continue with our explanation, let’s assume the value of 84 Here 84 is considered as a non-perfect square root since it contain either decimal or fraction. Let's learn more about square roots in this article.
What is the square root of 84?
The square root of 84 can be easily found out by using long division method. In which it is discovered that the cumulative approximation of √84 is 9.165.
Finding the square root of 84.
There are many ways through which students can find square roots, and some of these methods are very popular. Some of the methods have been explained in detail below.
Square root of 84 using the prime factorization method.
In this method, we decompose the number into its prime factors.
Prime factorization of 84: 84=2×2×3×7
Since not all prime factors can be paired, 84 cannot be simplified into a perfect square. Therefore, the square root of 84 cannot be expressed in a simple radical form.
Square root of 84 using the division method.
For non-perfect squares, we often use the nearest perfect square to estimate the square root. Follow these steps:
Step 1: Write the number 84 to perform long division.
Step 2: Identify a perfect square number that is less than or equal to 84. For 84, that number is 64 (8²).
Step 3: Divide 84 by 8. The remainder will be 20, and the quotient will be 10.
Step 4: Bring down the remainder (20) and append two zeros. Add a decimal point to the quotient, making it 10.0.
Step 5: Double the quotient to use as the new divisor, which gives 20.
Step 6: Select a number that, when multiplied by the new divisor, results in a product less than or equal to 2000.
Step 7: Continue the division process to find √84 to the desired decimal places. → √84 ≈ 9.165.
Square root of 84 using the approximation method
In the approximation method, we estimate the square root by identifying the closest perfect squares surrounding the number.
Step 1: The nearest perfect squares to 84 are √100 = 10 and √81 = 9.
Step 2: Since 84 is between 100 and 81, we know the square root will be between 10 and 9.
Step 3: By testing numbers like 9.1, 9.2 and further, we find that √84 ≈ 9.165.
Common mistakes when finding the square root of 84.
Here are some common mistakes students should avoid while learning to calculate the square root of 84.
Mistake 1
Confusing Square Roots with Cubes
It's a pretty common mistake where students get confused between square and cube root, one must remember that square root is represented as (√) and cube root is represented as (∛).
Square root of 84 Example
Problem 1
Is √50 a rational or irrational number?
→√50 is an irrational number
Explanation
while √50 can be simplified into 5√2, √2 is still irrational, therefore √50 is also an irrational number.
Problem 2
If x²= 49, what is x
x= ±7
Explanation
Solving x2=49 gives two possible solutions, x= 7, because both values squared result in 49.
Problem 3
What is the square of 9?
→ 81
Explanation
Finding a square of 9 is quite easy as it is a whole number, all you do is multiply it by itself, and hence the answer is 81.
FAQs on the square root of 84.
1.Name all the divisors of 84.
2.9 is the square root of what number?
3.What is the prime factorization of 84?
4. Is 84 a composite number?
5.What is the square root of 25?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Square root of 84.?
8.How do technology and digital tools in Singapore support learning Algebra and Square root of 84.?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for Square Root of 84.
- Square Root: A number which when is multiplied by itself gives the original number is called a square root.
- Perfect Square: A number that is the integral square of an integer I such that n = I², example I = 1, 2, 3, n = 1, 4, 9, 16, etc.
- Prime Factorization: The ability to factorize a number in to the product of the basic arithmetic numbers, also known as primary numbers.
- Non-Perfect Square: A figure that cannot be converted into an integer figure once divided by itself (e.g., 76).
- Approximation Method: Approximating square root, that is, finding the closest integer which, when squared, yields the number being approximated.
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About BrightChamps in Singapore
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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
