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159 LearnersLast updated on January 21st, 2025
Cube Root of 46
The cube root of a number is a value that, when multiplied three times by itself, gives the original number. Cube Root is used in many fields and subjects like; Engineering, Physics, Mechanics, and Cryptography. In this article, let us learn about the cube root of 46.
What Is the Cube Root of 46?
The Cube Root of a number is a value that, when multiplied three times by itself, gives the original number. So that means, the cube root of 46 is 3.5830. To understand it better let us convert it into an equation, consider a as the cube root of the number b, so the equation would be a3 = b.
In this case, the cube root of 46 is almost equal to 3.583, to show this like the equation as stated above: 3.583 × 3.583 × 3.583 ≈ 46. This is mostly used while studying three-dimensional shapes and the purpose of computing in many designs and learning problems.
The cube root is represented using the symbol, ∛ and the exponent used to denote it is ⅓. In exponential form, ∛46 is written as (46)1/3. The cube root is said to be the inverse operation of cubing a number.
Finding the Cube Root of 46
To find the cube root of a number, we use various methods. But to use these methods, it mainly depends on the properties of the number, like if the number is a perfect cube or not. As we are calculating the cube root for 46 we would use Halley’s method. Let us now see the methods that we use to find the cube root of 46.
- Prime factorization method
- Approximation method
- Halley’s method
- Subtraction method
Cube Root of 46 By Halley’s Method
One of the methods used to find non-perfect cubes is Halley’s method. As 46 is not a perfect cube we are using this method.
∛a≅ x((x3+2a) / (2x3+a)) here,
a = cube root of the given number
x = the nearest perfect cube
Here, a = 46; x = 3
∛a ≅ 3 ((33 + 2 × 46) / (2 × 33+ 46))
∛46 ≅ 3 ((27 + 2 × 46) / (2 × 27 + 46))
∛46 ≅ 3 (119/100)
∛46 ≅ 3 × 1.19
∛46 ≅ 3.57
The value of the cube root of 46 is 3.57
Common Mistakes and How to Avoid Them in the Cube Root of 46
Calculating the cube root is an important topic, but students will face some problems. A few common mistakes you should look out for when calculating the cube root of a number.
Mistake 1
Getting Confused with the Cube Root and Square Root
Sometimes students by mistake multiply a number by itself twice instead of three times. Which makes it a square root and not a cube root. So, if the students want to avoid this mistake, they must have good practice of finding the square roots and cube roots. For example, √46 = 6.782 (6.782 × 6.782 ≈ 46 ); ∛46 = 3.58 (3.58 × 3.58 × 3.58 ≈ 46)
Cube Root of 46 Examples
Problem 1
What is the value of ∛46 ÷ ∛(-46)
-1
Explanation
The cube root of -46 is equal to the negative of the cube root of 46.
⇒ ∛-46 = -∛46
Therefore,
⇒ ∛46/∛(-46) = ∛46/(-∛46) = -1
Problem 2
The Volume of a cube is 46 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 = ∛46
⇒ side of the cube = 3.58 cm
Therefore, the answer is 3.58 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 ∛46 - ∛49
∛46 - ∛49 = 3.58 – 3.65 = -0.07
Answer: -0.07
Explanation
We know that when we subtract the larger value from the smaller value, the result will be negative.
Problem 4
What is ∛(46)² ?
∛(46)2 = 3.582 = 12.83
Explanation
We first found the cube root of 46, which is 3.58, and then found out the square value of 3.58.
Problem 5
Find ∛(46+46).
∛(46+46) = ∛92 ≈ 4.52
Answer: 4.52
Explanation
As shown in the question ∛(46+46), we can simplify that by adding them. So, 46 + 46 = 92. Then we use this step: ∛92 ≈ 4.52 to get the answer.
FAQs on 46 Cube Root
1.Is 46 a perfect cube or not?
2.How to calculate ∛ ?
3.Determine whether the cube root of 46 is irrational.
4.What is 2% of 46?
5.Write the formula to find the cube of a number?
Important Glossaries for Cube Root of 46
- Perfect cube: A perfect cube of a number is the value, when the number is multiplied three times by itself and does not have any decimal point. For example, the number 27 is a perfect cube as 3 × 3 × 3 = 27.
- Irrational Number: An irrational number is a number that cannot be written in a fraction form or has a decimal point. For example, the cube root of 46 is 3.583 which is an irrational number.
- Rounding: To round the cube root before the entire calculation might be a wrong answer. The right way is to finish the entire calculation first, then round off the value.
- Exponent form: It is a way to express a number using powers. For example, for 23 here 3 is the power and the number 2 is the base value. Therefore, the exponent is 2.
- Whole numbers: Whole numbers are numbers that do not contain a decimal point and can be written in fraction form. For example, 1, 2, 3, 4, 5 and so on. All natural numbers are whole numbers but remember that all whole numbers are not natural numbers.
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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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
