5 Cubed In Exponential Form

Cube Root of 5

The value of the cube root of 5 rounded to half dozen decimal places is one.709976. Information technology is the real solution of the equation ten^three = 5. The cube root of 5 is expressed as ∛v in the radical form and every bit (5)^⅓ or (v)^0.33 in the exponent form. The prime factorization of 5 is five, hence, the cube root of 5 in its lowest radical form is expressed equally ∛5.

Cube root of 5: 1.709975947
Cube root of v in Exponential Course: (5)^⅓
Cube root of 5 in Radical Form: ∛5

Cube Root of 5

1.	What is the Cube Root of v?
2.	How to Calculate the Cube Root of 5?
iii.	Is the Cube Root of 5 Irrational?
4.	FAQs on Cube Root of 5

What is the Cube Root of five?

The cube root of 5 is the number which when multiplied past itself 3 times gives the product equally 5. The number v is prime. Therefore, the cube root of 5 = ∛5 = 1.71.

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How to Calculate the Value of the Cube Root of 5?

Cube Root of five by Halley'south Method

Its formula is ∛a ≈ ten ((x³ + 2a)/(2xⁱⁱⁱ + a))
where,
a = number whose cube root is being calculated
10 = integer guess of its cube root.

Here a = 5
Let us assume x equally i
[∵ ane³ = 1 and ane is the nearest perfect cube that is less than 5]
⇒ x = one
Therefore,
∛5 = 1 (1³ + 2 × 5)/(2 × 1³ + 5)) = ane.57
⇒ ∛5 ≈ ane.57
Therefore, the cube root of 5 is 1.57 approximately.

Is the Cube Root of 5 Irrational?

Yes, because ∛5 cannot be expressed in the grade of p/q where q ≠ 0. Therefore, the value of the cube root of v is an irrational number.

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Cube Root of 5 Solved Examples

Example 1: Find the real root of the equation 10³ − v = 0.

Solution:

xⁱⁱⁱ − 5 = 0 i.e. x³ = 5
Solving for 10 gives united states,
x = ∛5, x = ∛v × (-1 + √3i))/2 and x = ∛5 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛5
Therefore, the real root of the equation ten^three − 5 = 0 is for ten = ∛v = 1.71.
Example two: Given the volume of a cube is 5 in^three. Observe the length of the side of the cube.

Solution:

Volume of the Cube = 5 in^three = a³
⇒ a³ = v
Cube rooting on both sides,
⇒ a = ∛5 in
Since the cube root of five is 1.71, therefore, the length of the side of the cube is i.71 in.
Example 3: What is the value of ∛5 ÷ ∛(-five)?

Solution:

The cube root of -5 is equal to the negative of the cube root of 5.
⇒ ∛-5 = -∛5

Therefore,
⇒ ∛5/∛(-5) = ∛five/(-∛5) = -1

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FAQs on Cube Root of 5

What is the Value of the Cube Root of 5?

The value of the cube root of v is 1.70998.

Why is the Value of the Cube Root of 5 Irrational?

The value of the cube root of 5 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛5 is irrational.

What is the Cube of the Cube Root of 5?

The cube of the cube root of 5 is the number 5 itself i.e. (∛5)³ = (v^i/3)³ = v.

Is five a Perfect Cube?

The number 5 is prime number. Here, the prime factor five is not in the power of 3 and this implies that the cube root of 5 is irrational, hence 5 is not a perfect cube.

What is the Cube Root of -5?

The cube root of -5 is equal to the negative of the cube root of five. Therefore, ∛-v = -(∛5) = -(1.71) = -1.71.

What is the Value of i Plus 7 Cube Root 5?

The value of ∛5 is 1.71. So, 1 + 7 × ∛v = 1 + 7 × 1.71 = 12.969999999999999. Hence, the value of ane plus 7 cube root 5 is 12.969999999999999.