Cube Root of 1331

Cube Root of 1331 is 11. Cube Root of a number is represented in the form of ∛x so when it is multiplied twice with itself gives rise to the original number x. This means, when 11 is multiplied twice with 11 the product is 1331.

What is Cube Root of 1331?

Cube Root of 1331 is the number which when multiplied twice with itself gives 1331. We find that when 11 is multiplied twice by itself gives 11. Hence, cube root of 1331 is 11 The different ways in which the cube root of 1331 can be represented is given below:

• Radical Form of Cube Root of 1331: ∛1331 = 11
• Fractional Exponent Form of Cube Root of 1331 = (1331)^1/3 = 11

Cube Root of 1331 Calculator

Try out the following calculator to find the cube root of 1331

How to Calculate the Value of the Cube Root of 1331?

We can calculate cube root of 1331 using following two methods:

• Prime Factorization Method
• Long Divison Method

Learn, Cube and Cube Roots

Cube Root of 1331 By Prime Facrtorization

Use the following steps to find the cube root of 1331

Step 1: Determine the prime factorization of 1331 = 11 × 11 × 11

Step 2: Group the prime factors of 1331 in groups of three each. 1331 = (11 × 11 × 11)

Step 3: Use the law of exponents: 1331 = (11³)^1/3

Therefore, the cube root of 1331 by prime factorization is (11 × 11 × 11 )^1/3 = 11.

Cube Root of 1331 By Long Division Method

Use the following steps to find the cube root of 1331 by Long Division Method

Step 1: Begin by grouping the digits of the number 1331 in sets of three, starting from the right

Step 2: Find a number whose cube is less than or equal to the leftmost group. In this case, the cube of 1 is 1, which is less than 1331.

Step 3: Write the cube root (1) above the division symbol and subtract the cube (1) from the leftmost group

Step 4: Bring down the next group of digits to the right of the remainder

Step 5: Double the current quotient (1) and write it next to the previous quotient

Step 6: Guess a digit to add to the current quotient, which, when multiplied by the doubled quotient, gives a result less than or equal to the current remainder. In this case, the closest digit is 4 because 204 × 4 = 816, which is less than 831.

Step 7: Write the guessed digit (4) above the division symbol and multiply it by the doubled quotient

Step 8: Subtract the result from the previous remainder and bring down the next group of digits:

Step 9: Repeat steps 5 to 8 until you have obtained the desired level of precision or until the remainder becomes zero.

Continue the process until you reach the desired level of precision or until the remainder becomes zero. In this case, the cube root of 1331 is 11.

So, using the division method, you find that the cube root of 1331 is 11.

Is the Cube Root of 1331 Irrational?

No, because ∛1331 = ∛(11 × 11 × 11 ) can be expressed in the form of p/q i.e. 11/1. Therefore, the value of the cube root of 1331 is an integer (rational).

Cube Root of 1331 Solved Examples

Example 1: Look for the authentic root for equation x³ – 1331 = 0

Solution:

x = ∛1331

Thus, x = ∛1331 = ∛(1331 ) = 11 is the actual root of the equation x³ − 1331 = 0.

Example 2: The largest possible volume for a sphere is 1331 π cm³. What is ball’s radius?

Solution:

Volume of the spherical ball = 1331 π cm³

= 4/3 × π × R³

⇒ R³ = 3/4 × 1331

⇒ R = ∛(3/4 × 1331) = ∛(3/4) × ∛1331 = 0.90856 × 4 (∵ ∛(3/11) = 998.25and ∛1331 = 11)

⇒ R = 10.5 in³

Example 3: What would be the value √(-1331)

Solution:

The cube root of -1331 is equal to the negative of the cube root of 1331

⇒ ∛-1331= -∛1331

Therefore,

⇒ ∛1331 / ∛(-1331) = ∛1331 / (-∛1331) = -11

Cube Root of 1331 Practice Questions

Q1. Find if Cube Root of 1331 Minus Cube Root of 8 is a Rational Number?

Q2. If the Cube Root of 1331 is 11 , Find the Value of ∛0.01331.

Q3. Simplify the Cube Root of 1331/125

Cube Root of 1331 FAQs

What is Value of the Cube Root of 1331?

The value of the cube root of 1331 is 11.

What is Cube Root of a Number?

Cube Root of a number is the number which when multiplied twice with itself gives the original number

Is 1331 a Perfect Cube?

The number 1331 on prime factorization gives 11 × 11× 11 . Combining the prime factors in groups of 3 gives 11. So, the cube root of 1331 is a perfect cube

Why is Cube Root of 1331 Rational?

The value of the cube root of 1331 can be expressed in the form of p/q i.e. = 11/1, where q ≠ 0. Therefore, the ∛1331 is rational.

Is -11 a Cube Root of 1331?

No, -11 is not a cube root of 1331 because cube of -11 i.e. -11 × -11× -11 = -1331 which is not equal to 1331