The cube root of 9 is the number that is when multiplied three times to itself gives the result 9. Let x be the cube root of 9, then ∛9 = x and x3 = 9. The sign “√” is called the radical often used to represent the nth root of a number and “∛” is used to represent the cube root of a number.
The cube root of 9 in exponential form is written as 91/3. Let us learn how to find the cube root of 9.
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Cube Root of 9 |
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Cube of 9 |
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What is the Cube Root of 9?
The cube root of 9 is the number whose cube is 9. A perfect cube is a number which is the cube of an integer. Since we cannot find any integer whose cube is 9, therefore 9 is not a perfect cube number. Learn the cube root of 9 and also learn how to calculate the cube root of 9.
Check the cubes of numbers from 1 to 50.
How to Find the Cube Root of 9?
The cube root of 9 is not a rational number as we cannot find any integer whose cube is 9. Thus we cannot use the prime factorisation method to find the cube root of 9. To calculate the cube root of 9 we are going to Halley’s method whose formula is given by:
Halley Formula for Cube Root: ∛a ≈ x[(x3 + 2a)/(2x3 + a)]
Where a = the number whose cube root is to be determined.
x = is the guess number which is the cube root of the nearest perfect cube.
Now, let us calculate the cube root of 9 by Halley’s method. Here a = 9 and 23 = 8 < 9 we take x = 2. Let us put these values in the above formula, we get
∛9 = 2[(23 + 2 × 9)/(2 × 23 + 9)]
= 2[(8 + 18)/(16 + 9)]
= 2[(26)/(25)] = 2.83.
⇒ ∛25 = 2.83 (approx)
Video Lesson on Finding Cube Roots
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Solved Examples on Cube Root of 9
Example 1:
Find a real root of the equation y3 – 9 = 0.
Solution:
Given equation, y3 – 9 = 0
⇒ y3 = 9
Taking cube roots on both sides we get,
⇒ y = ∛9
The cube root of 9 is 2.0801 (approx.). The real cube root of the given equation is 2.0801.
Example 2:
Find the length of the side of the cube whose volume is 9 cm3.
Solution:
Let x be the side of the cube.
Volume of the cube = x3 = 9 cm3
⇒ x = ∛9 = 2.08 cm (approx.)
Example 3:
Find the base area of the cone whose height is equal to its base radius and volume is 3𝜋 cm3.
Solution:
Let r be the base radius of the cone.
The height of the cone is also r.
The volume of the cone = ⅓ 𝜋 r2 r = 3𝜋
⇒ r3 = (3𝜋)/(3. 1/𝜋) = 9
⇒ r = ∛9 = 2.08 (approx.)
∴ base area of the cone = 𝜋r2 = 3.14 × (2.08)2 ≈ 13.585 cm2.
Frequently Asked Questions on Cube Root of 9
What is the cube root of 9?
The cube root of 9 is approximately equal to 2.08.
Is 9 a perfect cube number?
No, 9 is not a perfect cube number.
Is the cube root of 9 a whole number?
No, the cube root of 9 is not a whole number, ∛9 = 2.0801 (approx.).
Is the cube root of 9 a rational number?
No, the cube root of 9 is an irrational number.
Can we find the cube root of 9 by the prime factorisation method?
No, we cannot the cube root of 9 by the prime factorisation method. We can use the approximation method or Halley’s formula to find the cube root.
What is cube number of 9?
The cube of 9 is 729.
