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Cube Root of 49

The value of the cube root of 49 rounded to 7 decimal places is 3.6593057. It is the real solution of the equation x3 = 49. The cube root of 49 is expressed as ∛49 in the radical form and as (49)⅓ or (49)0.33 in the exponent form. The prime factorization of 49 is 7 × 7, hence, the cube root of 49 in its lowest radical form is expressed as ∛49.

  • Cube root of 49: 3.65930571
  • Cube root of 49 in Exponential Form: (49)⅓
  • Cube root of 49 in Radical Form: ∛49

Cube Root of 49

1. What is the Cube Root of 49?
2. How to Calculate the Cube Root of 49?
3. Is the Cube Root of 49 Irrational?
4. FAQs on Cube Root of 49

What is the Cube Root of 49?

The cube root of 49 is the number which when multiplied by itself three times gives the product as 49. Since 49 can be expressed as 7 × 7. Therefore, the cube root of 49 = ∛(7 × 7) = 3.6593.

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How to Calculate the Value of the Cube Root of 49?

Cube Root of 49 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 = 49
Let us assume x as 3
[∵ 33 = 27 and 27 is the nearest perfect cube that is less than 49]
⇒ x = 3
Therefore,
∛49 = 3 (33 + 2 × 49)/(2 × 33 + 49)) = 3.64
⇒ ∛49 ≈ 3.64
Therefore, the cube root of 49 is 3.64 approximately.

Is the Cube Root of 49 Irrational?

Yes, because ∛49 = ∛(7 × 7) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 49 is an irrational number.

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Cube Root of 49 Solved Examples

  1. Example 1: Find the real root of the equation x3 − 49 = 0.

    Solution:

    x3 − 49 = 0 i.e. x3 = 49
    Solving for x gives us,
    x = ∛49, x = ∛49 × (-1 + √3i))/2 and x = ∛49 × (-1 - √3i))/2
    where i is called the imaginary unit and is equal to √-1.
    Ignoring imaginary roots,
    x = ∛49
    Therefore, the real root of the equation x3 − 49 = 0 is for x = ∛49 = 3.6593.

  2. Example 2: What is the value of ∛49 + ∛(-49)?

    Solution:

    The cube root of -49 is equal to the negative of the cube root of 49.
    i.e. ∛-49 = -∛49

    Therefore, ∛49 + ∛(-49) = ∛49 - ∛49 = 0

  3. Example 3: Given the volume of a cube is 49 in3. Find the length of the side of the cube.

    Solution:

    Volume of the Cube = 49 in3 = a3
    ⇒ a3 = 49
    Cube rooting on both sides,
    ⇒ a = ∛49 in
    Since the cube root of 49 is 3.66, therefore, the length of the side of the cube is 3.66 in.

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FAQs on Cube Root of 49

What is the Value of the Cube Root of 49?

We can express 49 as 7 × 7 i.e. ∛49 = ∛(7 × 7) = 3.65931. Therefore, the value of the cube root of 49 is 3.65931.

What is the Cube of the Cube Root of 49?

The cube of the cube root of 49 is the number 49 itself i.e. (∛49)3 = (491/3)3 = 49.

Why is the Value of the Cube Root of 49 Irrational?

The value of the cube root of 49 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛49 is irrational.

What is the Cube Root of -49?

The cube root of -49 is equal to the negative of the cube root of 49. Therefore, ∛-49 = -(∛49) = -(3.659) = -3.659.

How to Simplify the Cube Root of 49/27?

We know that the cube root of 49 is 3.65931 and the cube root of 27 is 3. Therefore, ∛(49/27) = (∛49)/(∛27) = 3.659/3 = 1.2197.

What is the Value of 15 Plus 20 Cube Root 49?

The value of ∛49 is 3.659. So, 15 + 20 × ∛49 = 15 + 20 × 3.659 = 88.17999999999999. Hence, the value of 15 plus 20 cube root 49 is 88.17999999999999.

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