201 LearnersLast updated on May 26th, 2025
Cube Root of 225
We will learn the cube root concept to use it on other mathematical topics like algebra, mensuration, geometry, trigonometry, etc. So, it is as important as learning square roots. Let us now see how we can obtain the cube root value of 225, and its examples.
What Is the Cube Root of 225?
The cube root of 225 is the value which, when multiplied by itself three times (cubed), gives the original number 225. The cube root of 225 is 6.08220199557. The cube root of 225 is expressed as ∛225 in radical form, where the “ ∛ ” sign” is called the “radical” sign. In exponential form, it is written as (225)â…“. If “m” is the cube root of 225, then, m3=225. Let us find the value of “m”.
Finding the Cube Root of 225
We can find cube roots of 225 through a method, named as, Halley’s Method. Let us see how it finds the result.
Cubic Root of 225 By Halley’s Method
Now, what is Halley’s Method? It is an iterative method for finding cube roots of a given number N, such that, x3=N, where this method approximates the value of “x”.
Formula is ∛a≅ x((x3+2a) / (2x3+a)), where
a=given number whose cube root you are going to find
x=integer guess for the cubic root
Let us apply Halley’s method on the given number 225.
Step 1: Let a=225. Let us take x as 6, since 63=216 is the nearest perfect cube which is less than 216.
Step 2: Apply the formula. ∛216≅ 6((63+2×225) / (2(6)3+225)) = 6.08…
Hence, 6.08… is the approximate cubic root of 225.
Common Mistakes and How to Avoid Them in the Cube Root of 225
Understanding common misconceptions or mistakes can make your calculations error free. So let us see how to avoid those from happening.
Mistake 1
For ∛225, students can make error in the important part of prime factorization.
Prime Factorization is a crucial part in determining cube roots and square roots. So, use the exact prime factors and group (or pair).
Cube Root of 225 Examples
Problem 1
Find ∛225/ ∛220
∛225/ ∛220
= 6.08 / 6.03
= 608/603
=1.008
Answer: 1.008
Explanation
We found that the cubic root of 220 is 6.03…, hence dividing ∛225 by ∛220.
Problem 2
The volume of a cube is 225 cubic centimeters, find the length of one side of the cube.
We know that, (side of a cube)3=Volume of a cube
⇒side of the cube = ∛(Volume of the cube)
⇒side of the cube = ∛225
⇒ side of the cube = 6.08 cm
Answer: 6.08 cm
Explanation
We applied the formula for finding the volume of a cube, and inverted it to find the measure of one side of the cube.
Problem 3
Subtract ∛225 - ∛216, ∛343-∛225
∛225-∛216
= 6.08–6
= 0.08
∛343-∛225
= 7-6.08
= 0.92
Answer: 0.08, 0.92
Explanation
We know that the cubic root of 216 is 6, hence subtracting ∛216 from ∛225.Applying the same for the next one, we know that the cubic root of 343 is 7, hence subtracting ∛225 from ∛343.
Problem 4
What is ∛(225²) ?
∛(2252) = (225)2/3
Answer:(225)2/3
Explanation
Converted the given expression into its exponential form.
Problem 5
Find ∛(225+118).
∛(225+118)
= ∛343
=7
Answer: 7
Explanation
Simplified the expression, and found out the cubic root of the result.
FAQs on 225 Cube Root
1.What is 5√225 simplified ?
2.Can the ∛225 be simplified ?
3.What will be the cube of 225?
4.How to solve the cube root of 25?
5.How is ∛225 irrational?
6.How does learning Algebra help students in Indonesia make better decisions in daily life?
7.How can cultural or local activities in Indonesia support learning Algebra topics such as Cube Root of 225?
8.How do technology and digital tools in Indonesia support learning Algebra and Cube Root of 225?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for Cube Root of 225
- Cube root properties - The features when cube root is applied to any number. Those are: 1) The cube root of all odd numbers is an odd number. The same applies for even numbers also, that is, the cube of any even number is even.
2) The cube root of a negative number is also negative.
3) If the cube root of a number is a whole number, then that original number is said to be perfect cube
- Irrational Numbers - Numbers which cannot be expressed as m/n form, where m and n are integers and n not equal to 0, are called Irrational numbers.
- Square root -The square root of a number is a number which when multiplied by itself produces the original number, whose square root is to be found out.
- Polynomial - It is an algebraic expression made up of variables like “x” and constants, combined using addition, subtraction, multiplication, or division, where the variables are raised to whole number exponents.
- Approximation - Finding out a value which is near to the correct answer, but not perfectly correct.
- Iterative method - This method is a mathematical process which uses an initial value to generate a further sequence of solutions for a problem, step-by-step.
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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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