Cube Root of 45
The value of the cube root of 45 rounded to 5 decimal places is 3.55689. It is the real solution of the equation x^{3} = 45. The cube root of 45 is expressed as ∛45 in the radical form and as (45)^{⅓} or (45)^{0.33} in the exponent form. The prime factorization of 45 is 3 × 3 × 5, hence, the cube root of 45 in its lowest radical form is expressed as ∛45.
 Cube root of 45: 3.556893304
 Cube root of 45 in Exponential Form: (45)^{⅓}
 Cube root of 45 in Radical Form: ∛45
1.  What is the Cube Root of 45? 
2.  How to Calculate the Cube Root of 45? 
3.  Is the Cube Root of 45 Irrational? 
4.  FAQs on Cube Root of 45 
What is the Cube Root of 45?
The cube root of 45 is the number which when multiplied by itself three times gives the product as 45. Since 45 can be expressed as 3 × 3 × 5. Therefore, the cube root of 45 = ∛(3 × 3 × 5) = 3.5569.
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How to Calculate the Value of the Cube Root of 45?
Cube Root of 45 by Halley's Method
Its formula is ∛a ≈ x ((x^{3} + 2a)/(2x^{3} + a))
where,
a = number whose cube root is being calculated
x = integer guess of its cube root.
Here a = 45
Let us assume x as 3
[∵ 3^{3} = 27 and 27 is the nearest perfect cube that is less than 45]
⇒ x = 3
Therefore,
∛45 = 3 (3^{3} + 2 × 45)/(2 × 3^{3} + 45)) = 3.55
⇒ ∛45 ≈ 3.55
Therefore, the cube root of 45 is 3.55 approximately.
Is the Cube Root of 45 Irrational?
Yes, because ∛45 = ∛(3 × 3 × 5) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 45 is an irrational number.
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Cube Root of 45 Solved Examples

Example 1: Find the real root of the equation x^{3} − 45 = 0.
Solution:
x^{3} − 45 = 0 i.e. x^{3} = 45
Solving for x gives us,
x = ∛45, x = ∛45 × (1 + √3i))/2 and x = ∛45 × (1  √3i))/2
where i is called the imaginary unit and is equal to √1.
Ignoring imaginary roots,
x = ∛45
Therefore, the real root of the equation x^{3} − 45 = 0 is for x = ∛45 = 3.5569. 
Example 2: Given the volume of a cube is 45 in^{3}. Find the length of the side of the cube.
Solution:
Volume of the Cube = 45 in^{3} = a^{3}
⇒ a^{3} = 45
Cube rooting on both sides,
⇒ a = ∛45 in
Since the cube root of 45 is 3.56, therefore, the length of the side of the cube is 3.56 in. 
Example 3: The volume of a spherical ball is 45π in^{3}. What is the radius of this ball?
Solution:
Volume of the spherical ball = 45π in^{3}
= 4/3 × π × R^{3}
⇒ R^{3} = 3/4 × 45
⇒ R = ∛(3/4 × 45) = ∛(3/4) × ∛45 = 0.90856 × 3.55689 (∵ ∛(3/4) = 0.90856 and ∛45 = 3.55689)
⇒ R = 3.23165 in^{3}
FAQs on Cube Root of 45
What is the Value of the Cube Root of 45?
We can express 45 as 3 × 3 × 5 i.e. ∛45 = ∛(3 × 3 × 5) = 3.55689. Therefore, the value of the cube root of 45 is 3.55689.
Why is the Value of the Cube Root of 45 Irrational?
The value of the cube root of 45 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛45 is irrational.
What is the Value of 20 Plus 4 Cube Root 45?
The value of ∛45 is 3.557. So, 20 + 4 × ∛45 = 20 + 4 × 3.557 = 34.228. Hence, the value of 20 plus 4 cube root 45 is 34.228.
How to Simplify the Cube Root of 45/64?
We know that the cube root of 45 is 3.55689 and the cube root of 64 is 4. Therefore, ∛(45/64) = (∛45)/(∛64) = 3.557/4 = 0.8892.
If the Cube Root of 45 is 3.56, Find the Value of ∛0.045.
Let us represent ∛0.045 in p/q form i.e. ∛(45/1000) = 3.56/10 = 0.36. Hence, the value of ∛0.045 = 0.36.
Is 45 a Perfect Cube?
The number 45 on prime factorization gives 3 × 3 × 5. Here, the prime factor 3 is not in the power of 3. Therefore the cube root of 45 is irrational, hence 45 is not a perfect cube.
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