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

Cube Root of 686

The value of the cube root of 686 rounded to 5 decimal places is 8.81945. It is the real solution of the equation x³ = 686. The cube root of 686 is expressed as ∛686 or 7 ∛2 in the radical form and as (686)^⅓ or (686)^0.33 in the exponent form. The prime factorization of 686 is 2 × 7 × 7 × 7, hence, the cube root of 686 in its lowest radical form is expressed as 7 ∛2.

Cube root of 686: 8.819447349
Cube root of 686 in Exponential Form: (686)^⅓
Cube root of 686 in Radical Form: ∛686 or 7 ∛2

1.	What is the Cube Root of 686?
2.	How to Calculate the Cube Root of 686?
3.	Is the Cube Root of 686 Irrational?
4.	FAQs on Cube Root of 686

What is the Cube Root of 686?

The cube root of 686 is the number which when multiplied by itself three times gives the product as 686. Since 686 can be expressed as 2 × 7 × 7 × 7. Therefore, the cube root of 686 = ∛(2 × 7 × 7 × 7) = 8.8194.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 686?

Cube Root of 686 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 = 686
Let us assume x as 8
[∵ 8³ = 512 and 512 is the nearest perfect cube that is less than 686]
⇒ x = 8
Therefore,
∛686 = 8 (8³ + 2 × 686)/(2 × 8³ + 686)) = 8.81
⇒ ∛686 ≈ 8.81
Therefore, the cube root of 686 is 8.81 approximately.

Is the Cube Root of 686 Irrational?

Yes, because ∛686 = ∛(2 × 7 × 7 × 7) = 7 ∛2 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 686 is an irrational number.

☛ Also Check:

Cube Root of 686 Solved Examples

Example 1: The volume of a spherical ball is 686π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 686π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 686
⇒ R = ∛(3/4 × 686) = ∛(3/4) × ∛686 = 0.90856 × 8.81945 (∵ ∛(3/4) = 0.90856 and ∛686 = 8.81945)
⇒ R = 8.013 in³
Example 2: Given the volume of a cube is 686 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 686 in³ = a³
⇒ a³ = 686
Cube rooting on both sides,
⇒ a = ∛686 in
Since the cube root of 686 is 8.82, therefore, the length of the side of the cube is 8.82 in.
Example 3: What is the value of ∛686 ÷ ∛(-686)?

Solution:

The cube root of -686 is equal to the negative of the cube root of 686.
⇒ ∛-686 = -∛686

Therefore,
⇒ ∛686/∛(-686) = ∛686/(-∛686) = -1

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 686

What is the Value of the Cube Root of 686?

We can express 686 as 2 × 7 × 7 × 7 i.e. ∛686 = ∛(2 × 7 × 7 × 7) = 8.81945. Therefore, the value of the cube root of 686 is 8.81945.

Is 686 a Perfect Cube?

The number 686 on prime factorization gives 2 × 7 × 7 × 7. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 686 is irrational, hence 686 is not a perfect cube.

What is the Cube Root of -686?

The cube root of -686 is equal to the negative of the cube root of 686. Therefore, ∛-686 = -(∛686) = -(8.819) = -8.819.

If the Cube Root of 686 is 8.82, Find the Value of ∛0.686.

Let us represent ∛0.686 in p/q form i.e. ∛(686/1000) = 8.82/10 = 0.88. Hence, the value of ∛0.686 = 0.88.

Why is the Value of the Cube Root of 686 Irrational?

The value of the cube root of 686 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛686 is irrational.

What is the Value of 20 Plus 11 Cube Root 686?

The value of ∛686 is 8.819. So, 20 + 11 × ∛686 = 20 + 11 × 8.819 = 117.00900000000001. Hence, the value of 20 plus 11 cube root 686 is 117.00900000000001.