Cube Root of 40: Simplified Radical Form

The cube root of 40 in simplified radical form is equal to 2∛5. The value of cube root of 40 is 3.42 corrected up to two decimal places. Note that a number m is called a cube root of 40 if m³ = 40. So it is a root of the cubic equation x³=40, so there are three cube roots of 40.

Some facts are listed below:

• Cube root of 40 in simplified radical form is 2∛5.
• ∛40 = 2∛5.
• 40 is not a prefect cube number.
• 40^1/3 is the exponential for of the cube root of 40.
• Value of cube root of 40 is 3.4199 (in decimal form) corrected up to 4 decimal places.
• cube of 40: 40×40×40 = 64000.

What is the Cube Root of 40?

To find the cube root of 40, we will express the number 40 as a product of numbers at least one of them will be perfect cubes. We can write 40 as follows:

40 = 8×5.

Here 8 is a perfect cube as 8 = 2³.

Taking cube root on both sides, we obtain that

$\sqrt[3]{40} = \sqrt[3]{8 \times 5}$ ⇒ $\sqrt[3]{40} = \sqrt[3]{8} \times \sqrt[3]{5}$ using the rule: ∛ab = ∛a ∛b. ⇒ $\sqrt[3]{40} = 2 \times \sqrt[3]{5}$.

That is, ∛40 = 2∛5.

So the cube root of 40 in its simplified radical form is equal to 2∛5.

By Prime Factorization

The prime factorization of 40 is given as follows:

40 = 2 × 2 × 2 × 5.

So $\sqrt[3]{40} = \sqrt[3]{2 \times 2 \times 2 \times 5}$

Make a grouping of 3 identical numbers, so we obtain that

$\sqrt[3]{40} = \sqrt[3]{2 \times 2 \times 2} \times \sqrt[3]{5}$ ⇒ ∛40 = 2 × ∛5 ⇒ ∛40 = 2∛5.

So the cube root of 40 by prime factorization method is equal to 2∛5, and it is its simplest radical form.

More cube roots:

• Cube root of 125
• Cube root of 27

Value of Cube Root of 40

As we know that cube root of 40 is given by ∛40 = 2∛5, and the value of ∛5 is 1.71 approximately, so we obtain that

∛40 = 2 × 1.71 = 3.42.

Therefore, 3.42 is the value of cube root of 40.

Also Read: cube root of 81

Is 40 a Perfect Cube

Answer: Note that 40 will be a prefect cube number only if its cube root is a whole number. We know that ∛40 = 2∛5 is not a whole number. This proves that the number 40 is not a perfect cube.

Is Cube Root of 40 Rational

Answer: The cube root of 40 is 2∛5, and the number ∛5 is irrational. Therefore, we conclude that cube root of 40 is not a rational number.

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