A day full of math games & activities. Find one near you.

Cube Root of 162

The value of the cube root of 162 rounded to 6 decimal places is 5.451362. It is the real solution of the equation x³ = 162. The cube root of 162 is expressed as ∛162 or 3 ∛6 in the radical form and as (162)^⅓ or (162)^0.33 in the exponent form. The prime factorization of 162 is 2 × 3 × 3 × 3 × 3, hence, the cube root of 162 in its lowest radical form is expressed as 3 ∛6.

Cube root of 162: 5.451361778
Cube root of 162 in Exponential Form: (162)^⅓
Cube root of 162 in Radical Form: ∛162 or 3 ∛6

Cube Root of 162

1.	What is the Cube Root of 162?
2.	How to Calculate the Cube Root of 162?
3.	Is the Cube Root of 162 Irrational?
4.	FAQs on Cube Root of 162

What is the Cube Root of 162?

The cube root of 162 is the number which when multiplied by itself three times gives the product as 162. Since 162 can be expressed as 2 × 3 × 3 × 3 × 3. Therefore, the cube root of 162 = ∛(2 × 3 × 3 × 3 × 3) = 5.4514.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 162?

Cube Root of 162 by Halley's Method

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

Here a = 162
Let us assume x as 5
[∵ 5³ = 125 and 125 is the nearest perfect cube that is less than 162]
⇒ x = 5
Therefore,
∛162 = 5 (5³ + 2 × 162)/(2 × 5³ + 162)) = 5.45
⇒ ∛162 ≈ 5.45
Therefore, the cube root of 162 is 5.45 approximately.

Is the Cube Root of 162 Irrational?

Yes, because ∛162 = ∛(2 × 3 × 3 × 3 × 3) = 3 ∛6 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 162 is an irrational number.

☛ Also Check:

Cube Root of 162 Solved Examples

Example 1: What is the value of ∛162 + ∛(-162)?

Solution:

The cube root of -162 is equal to the negative of the cube root of 162.
i.e. ∛-162 = -∛162

Therefore, ∛162 + ∛(-162) = ∛162 - ∛162 = 0
Example 2: Find the real root of the equation x³ − 162 = 0.

Solution:

x³ − 162 = 0 i.e. x³ = 162
Solving for x gives us,
x = ∛162, x = ∛162 × (-1 + √3i))/2 and x = ∛162 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛162
Therefore, the real root of the equation x³ − 162 = 0 is for x = ∛162 = 5.4514.
Example 3: The volume of a spherical ball is 162π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 162π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 162
⇒ R = ∛(3/4 × 162) = ∛(3/4) × ∛162 = 0.90856 × 5.45136 (∵ ∛(3/4) = 0.90856 and ∛162 = 5.45136)
⇒ R = 4.95289 in³

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on Cube Root of 162

What is the Value of the Cube Root of 162?

We can express 162 as 2 × 3 × 3 × 3 × 3 i.e. ∛162 = ∛(2 × 3 × 3 × 3 × 3) = 5.45136. Therefore, the value of the cube root of 162 is 5.45136.

What is the Cube Root of -162?

The cube root of -162 is equal to the negative of the cube root of 162. Therefore, ∛-162 = -(∛162) = -(5.451) = -5.451.

How to Simplify the Cube Root of 162/343?

We know that the cube root of 162 is 5.45136 and the cube root of 343 is 7. Therefore, ∛(162/343) = (∛162)/(∛343) = 5.451/7 = 0.7787.

If the Cube Root of 162 is 5.45, Find the Value of ∛0.162.

Let us represent ∛0.162 in p/q form i.e. ∛(162/1000) = 5.45/10 = 0.55. Hence, the value of ∛0.162 = 0.55.

What is the Value of 19 Plus 13 Cube Root 162?

The value of ∛162 is 5.451. So, 19 + 13 × ∛162 = 19 + 13 × 5.451 = 89.863. Hence, the value of 19 plus 13 cube root 162 is 89.863.

Why is the Value of the Cube Root of 162 Irrational?

The value of the cube root of 162 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛162 is irrational.

Math worksheets and
visual curriculum