Cube root of 27

The cube root of 27 is a number when multiplied by itself two times will be 27. The cube root of 27 is denoted by the symbol ∛27. In this section, we will learn how to find the value of  ∛27.

Note that if a cube has a volume of 27 unit², then we use the cube root of 27 to find the length of the cube. The value of the cube root of 27 is 3.

Important Things:

• $\sqrt[3]{27} = 3$
• 27 is a perfect cube.
• $\sqrt[3]{27}$ is the surd form of cube root of 27.
• 27^1/3 is the exponential form of cube root of 27.
• The cube root of 27 is 3.000 in decimal form.
• cube of 27: 27×27×27 = 19683

Let us now calculate the cube root of 27.

What is the Cube Root of 27?

It is known that 27=3×3×3. As this is a product of three numbers of 3‘s, we can write

27=3³

Taking cube root on both sides, we have

$\sqrt[3]{27} = \sqrt[3]{3^3}$

We know that the cube root can be written as power 1/3. So we get that

$\sqrt[3]{27}$ = (3³)^1/3

= 3^3×1/3   as we know that (a^m)ⁿ = a^m×n

= 3¹ = 3

Thus the value of the cube root of 27 is 3.

 

Is 27 a perfect cube number?

From above we have that $\sqrt[3]{27}=3$. As 3 is a whole number, the cube root of 27 is also a whole number.

∴ the definition of a perfect cube implies that 27 is a perfect cube number.

 

Cube Root of 27 by Prime Factorization

Note that the cube root of 27 is 3. We will now use the prime factorization method to find it. At first, we will factorize the number 27. We have 

27=3×9 and 9=3×3.

So we deduce that

27=3×3×3.

As 3 is a prime number, we cannot factorize further. 

Taking cube root on both sides of (∗), we get that

$\sqrt[3]{27} = \sqrt[3]{3×3×3}$

= 3 as we know that $\sqrt[3]{a×a×a}=a$

∴  The cube root of 27 is 3. 

Question: What is the cube root of 27?

Video Solution:

Is Cube Root of 27 Rational?

We know that a number is a rational number if and only if it can be expressed as p/q where p and q are integers with q ≠ 0.

We have calculated above that $\sqrt[3]{27}=3$.

Note that 3=3/1

⇒ 3 can be written as p/q with p=3, q=1≠0.

⇒ 3 is a rational number.

⇒ the cube root of 27 is also a rational number.

Conclusion: The cube root of 27 is a rational number.

 

Key Things about 27

• 27 is a composite odd number.
• A cube of length 3 unit has the volume 27 unit³