The worth of the cube root of 144 rounded to 5 decimal locations is 5.24148. That is the real solution of the equation x3 = 144. The cube source of 144 is expressed as ∛144 or 2 ∛18 in the radical form and together (144)⅓ or (144)0.33 in the exponent form. The element factorization that 144 is 2 × 2 × 2 × 2 × 3 × 3, hence, the cube source of 144 in its shortest radical type is expressed as 2 ∛18.
You are watching: What is the cube root of 144
| 1. | What is the Cube root of 144? |
| 2. | How to calculate the Cube source of 144? |
| 3. | Is the Cube source of 144 Irrational? |
| 4. | FAQs top top Cube root of 144 |
What is the Cube source of 144?
The cube source of 144 is the number which once multiplied through itself three times provides the product together 144. Due to the fact that 144 deserve to be expressed together 2 × 2 × 2 × 2 × 3 × 3. Therefore, the cube root of 144 = ∛(2 × 2 × 2 × 2 × 3 × 3) = 5.2415.
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how to calculate the value of the Cube source of 144?
Cube source of 144 through Halley"s an approach
that is formula is ∛a ≈ x ((x3 + 2a)/(2x3 + a)) where, a = number whose cube source is being calculated x = integer assumption: v of that cube root.
here a = 144 Let us assume x as 5 <∵ 53 = 125 and also 125 is the nearest perfect cube that is less than 144> ⇒ x = 5 Therefore, ∛144 = 5 (53 + 2 × 144)/(2 × 53 + 144)) = 5.24 ⇒ ∛144 ≈ 5.24 Therefore, the cube root of 144 is 5.24 approximately.
Is the Cube root of 144 Irrational?
Yes, since ∛144 = ∛(2 × 2 × 2 × 2 × 3 × 3) = 2 ∛18 and also it can not be expressed in the type of p/q wherein q ≠ 0. Therefore, the value of the cube root of 144 is an irrational number.
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Cube source of 144 fixed Examples
instance 1: What is the worth of ∛144 ÷ ∛(-144)?
Solution:
The cube root of -144 is same to the an unfavorable of the cube source of 144. ⇒ ∛-144 = -∛144 Therefore, ⇒ ∛144/∛(-144) = ∛144/(-∛144) = -1
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FAQs top top Cube source of 144
What is the value of the Cube root of 144?
We can express 144 together 2 × 2 × 2 × 2 × 3 × 3 i.e. ∛144 = ∛(2 × 2 × 2 × 2 × 3 × 3) = 5.24148. Therefore, the value of the cube root of 144 is 5.24148.
Is 144 a Perfect Cube?
The number 144 on prime factorization provides 2 × 2 × 2 × 2 × 3 × 3. Here, the prime factor 2 is no in the power of 3. As such the cube source of 144 is irrational, for this reason 144 is not a perfect cube.
Why is the worth of the Cube source of 144 Irrational?
The worth of the cube source of 144 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛144 is irrational.
What is the Cube of the Cube source of 144?
The cube that the cube source of 144 is the number 144 chin i.e. (∛144)3 = (1441/3)3 = 144.
What is the Cube root of -144?
The cube root of -144 is same to the an unfavorable of the cube source of 144. Therefore, ∛-144 = -(∛144) = -(5.241) = -5.241.
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How to leveling the Cube root of 144/216?
We recognize that the cube source of 144 is 5.24148 and also the cube source of 216 is 6. Therefore, ∛(144/216) = (∛144)/(∛216) = 5.241/6 = 0.8735.