Cube Root of 512: Value, Calculation & Solved Examples

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Cube Root of 512 is 8. Cube root of 512 is a number that, when multiplied by itself three times, gives the product as 512.

Cube root of 512 is expressed as ∛512 in radical form.
In exponential form, it is expressed as (512)⅓ or (512)^0.33.
The method of prime factorization is used to calculate the cube root of 512.
Cube root of 512 is the real value of the equation x³ = 512.
The number 512 is a perfect cube because the cube root of the number is a whole number (8).

Table of Content

What is Cube Root of 512?
How to Find Cube Root of 512?
Is Cube Root of 512 Irrational?
Solved Examples on Cube Root of 512
Cubes From 1 to 10
Things to Remember
Sample Questions

Key Terms: Cube Root of 512, Multiplication, Cube Root, Natural Number, Prime Factorization, Cube, Exponential Form

What is Cube Root of 512?

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Cube Root of 512 is a natural number that gives the product as 512 on multiplication with itself thrice. Thus, the cube root of 512 is 8. The prime factors of the number 512 can be written as

512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

512 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2) = 2 x 2 x 2 = 8

Thus

Cube Root of 512: 8
Cube root of 512 in Radical Form: ∛512
Cube Root of 512 in Exponential Form: (512)^⅓ or (512)^0.33

Cube Root of 512

Cube Root of 512

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Cube and Cube Roots	Cube Root 1 to 30	Cube Root of 729
Cube Root of 64	Cube Root of 343	Cube Root 1 to 20

How to Find Cube Root of 512?

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Prime Factorization is used to find out the value of the cube root of 512. To find the cube root of 512, the same factors of the number are taken as a pair of three and then taken out as a single digit, as the cube of a number will cancel the cube root.

Here are the steps to calculate the cube root of 512:

Step 1: The prime factorization of 512 is 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2.
Step 2: on simplification of the above expression, we get 29
Step 3: On further simplification, we get 83.

Thus, the cube root of 512 is

512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

512 = (2 × 2 × 2) × (2 × 2 × 2) x (2 × 2 × 2)

512 = 2 x 2 x 2 = 8

Therefore, 8 is the cube root of 512.

Is Cube Root of 512 Irrational?

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No, the cube root of 512 is not irrational.

The cube root of 512 is 8.
512 is a perfect cube because its cube root is 8, which is a whole number.
It can be expressed as p/q i.e 8/1.
Thus, the cube of 512 is a rational number that can be expressed in the form of p/q where q is not equal to zero.

Read More: Cubes and Cube Roots MCQs

Solved Examples on Cube Root of 512

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Here are a few solved examples on the cube root of 512:

Example 1: What is the value of ∛512/∛125?

Solution: According to the question,

∛512/∛125 = Cube Root of 512 / Cube Root of 125 =?

We know that the cube root of 512 is 8 and the cube root of 125 is 5.

Thus,

(∛512)/(∛125) = 8/5 = 1.6

Thus, the value of ∛512/∛125 is 1.6.

Example 2: Simplify the given fraction, ∛(512/729).

Solution: The given fraction is ∛(512/729).

We know that 8 is the cube root of 512 and 9 is the cube root of 729.

Thus,

∛(512/729) = (∛512)/(∛729) = 8/9 or 0.8889.

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Finding Square Roots through Prime Factorization	Estimating Square Root	Root Mean Square
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Cubes From 1 to 10

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Given below are the cubes of the numbers from 1 to 10 to calculate the value of cube roots easily:

Number (n)	Cubes (n³)
1	1
2	8
3	27
4	64
5	125
6	216
7	343
8	512
9	729
10	1000

Read More: Cubes from 1 to 50

Things to Remember

Cube root of 512 is a number which when multiplied by itself thrice, gives 512 as the product.
Cube Root of 512 is 8.
Cube Root of 512 in radical form is ∛512.
The exponential form of the cube root of 512 is (512)^⅓ or (512)^0.33.
The cube root of 512, i.e. 8 is a whole number, thus, 512 is a perfect cube.

Sample Questions

Ques. The volume of a cube is 512 in³. Find the length of its sides. (2 Marks)

Ans. It is given that

Volume of Cube = a³ = 512

a³ = 512

Putting cube roots on both sides, we get

a = ∛512 = 8

Thus, the length of the side of the cube is 8 inches.

Ques. Find the radius of a spherical ball whose volume is 521π. (2 Marks)

Ans. Given that

Volume of Spherical Ball = 512π in³

512 = 4/3 × π × R³

R³ = 3/4 × 512

R = ∛(3/4 × 512)

R = ∛(3/4) × ∛512

R = 0.90856 × 8 [∵ ∛(3/4) = 0.90856 and ∛512 = 8]

R = 7.26848 in

Thus, the radius of the spherical ball is 7.26848 in

Ques. Show if 512 is a perfect cube. (2 Marks)

Ans. On prime factorization, 512 is expressed as

512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

Sorting the prime factors in pairs of three gives us 8, which is a whole number. Thus, 512 is a perfect cube.

Ques. Check whether the cube root of 512 is rational or irrational. (2 Marks)

Ans. The cube root value of 512 is rational. The value of the cube root of 512 is a whole number i.e. 8, which can be expressed in the form of p/q where q is not equal to zero. Thus, we can say that the cube root of 512 is rational.

Ques. Calculate the value of ∛512 ÷ ∛(-512). (2 Marks)

Ans. The cube root of -512 is equal to the negative of the cube root of 512.

∛-512 = -∛512

Thus,

∛512 ÷ ∛(-512)

= ∛512 ÷ (-∛512)

= 8 ÷ -8 = -1

Thus, the value of ∛512 ÷ ∛(-512) is -1.

Ques. 512 is not a perfect square. Explain. (2 Marks)

Ans. 512 is not a perfect square because it is a perfect cube. For a number to be a perfect square has to be a product of an integer with itself. For example 5 × 5 = 25.

The only numbers between 1 and 1000 that are perfect squares and cubes are 1, 64, and 729.

Ques. What is the cube root of 512? (2 Marks)

Ans. On prime factorization, 512 can be expanded as

512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

∛512 =∛(2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2)

On dividing the primes into triplet we get,

∛512= (2×2×2) (2×2×2) (2×2×2)

∛512= 2×2×2 (taking one value from each triplet.)

Therefore, the value of the cube root of 512 is 8.

Ques. What is the value of 7 plus 1 cube root 512? (2 Marks)

Ans. Let that number be x,

So,

x = 7 + 1 × ∛512

8 is the cube root of 512.

x = 7+(1×8)

x = 7+8

∵ x = 15

Therefore, the value of 7 plus 1 cube root 512 is 15.

Ques. What is the cube root of ∛-512? (2 Marks)

Ans. Negative numbers always have a negative cube root.

⇒ -512= - (2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2)

⇒ -512= - ( 23 X 23 X 23)= -83

⇒ ∛-512= ∛-83= - 8

Therefore, the cube root of -512 is -8.

Ques. Is 512 a prime or composite number? (2 Marks)

Ans. 512 is a composite number. It is because 512 has factors other than 1 and the number itself. There are 10 factors of the number 512. The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, and 512.

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Cube Root of 512: Value, Calculation & Solved Examples

What is Cube Root of 512?

How to Find Cube Root of 512?

Is Cube Root of 512 Irrational?

Solved Examples on Cube Root of 512

Cubes From 1 to 10

Things to Remember

Sample Questions

CBSE X Related Questions

1.
In the given figure, point D divides the side BC of $\Delta ABC$ in the ratio $1 : 2$. Find length AD.

2.
In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

3.
Two dice are rolled together. The probability of getting an outcome $(x, y)$ where $x \gt y$, is

4.
Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$

5.
A chord of a circle, of radius 14 cm, subtends an angle of $60^\circ$ at the centre. Find the area of the smaller sector and perimeter of the smaller segment.

6.
PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If OP = 13 cm, then find the length AB and PA.

Similar Mathematics Concepts

Comments

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Cube Root of 512: Value, Calculation & Solved Examples

What is Cube Root of 512?

How to Find Cube Root of 512?

Is Cube Root of 512 Irrational?

Solved Examples on Cube Root of 512

Cubes From 1 to 10

Things to Remember

Sample Questions

CBSE X Related Questions

1.In the given figure, point D divides the side BC of $\Delta ABC$ in the ratio $1 : 2$. Find length AD.

2.In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

3.Two dice are rolled together. The probability of getting an outcome $(x, y)$ where $x \gt y$, is

4.Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$

5.A chord of a circle, of radius 14 cm, subtends an angle of $60^\circ$ at the centre. Find the area of the smaller sector and perimeter of the smaller segment.

6.PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If OP = 13 cm, then find the length AB and PA.

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
In the given figure, point D divides the side BC of $\Delta ABC$ in the ratio $1 : 2$. Find length AD.

2.
In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

3.
Two dice are rolled together. The probability of getting an outcome $(x, y)$ where $x \gt y$, is

4.
Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$

5.
A chord of a circle, of radius 14 cm, subtends an angle of $60^\circ$ at the centre. Find the area of the smaller sector and perimeter of the smaller segment.

6.
PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If OP = 13 cm, then find the length AB and PA.