Cube Root of 343

Cube Root of 343 is 7. This is because 7 multiplied by itself three times (7 × 7 × 7) equals 343. Therefore, the cube root of 343 is the number that, when multiplied by itself three times, equals 343, and that number is 7. In this article, we will learn about Cube Root of 343, its value and methods to calculate it.

Cube Root Definition

In mathematical terms, if x represents the input value, then the cube root ∛x​, or simply written as x^1/3, yields the positive real number whose cube equals x.

What is the Cube Root of 343?

The cube root of 343 is worth 7. the real value of the equation x = 343 is x³ . The radical form of 343 cube root is ∛343 while (343)^1/3 or (343)^0.33 are its exponent forms. For the cube root of 343 being an integer, 343 is a perfect cube.

• Cube root of 343: 7
• Cube root of 343 in exponential form: (343)⅓
• Cube root of 343 in radical form: ∛343

Value of Cube Root of 343

he cube root of 343 is the number which when multiplied by itself three times gives the product as 343. Since 343 can be expressed as 7 × 7 × 7. Therefore, the cube root of 343 = ∛(7 × 7 × 7) = 7.

Cube Root Calculator

Cube root of any number can be calculated using the following calculator:

Methods to Calculate the Value of the Cube Root of 343

There are various methods to calculate cube root. But for 343 we can use Prime Factorization to calculate cube root of 343. Cube root of 343 is discussed as follows:

Cube Root of 343 By Prime Factorization

Use the following steps to find the cube root of 343

Step 1: Determine the prime factorization of 343.

Thus, prime factorization of 343 is 7 × 7 × 7.

Step 2: Group the prime factors of 343 in groups of three each i.e., 343= (7 × 7 × 7)

Step 3: Use the law of exponents: 343 = (343)^1/3

Therefore, the cube root of 343by prime factorization is (7 × 7 × 7 )^1/3 = 7.

Is the Cube Root of 343 Irrational?

Cube Root of 343 is not an irrational number. In fact, the cube root of 343 is equal to 7, which is a rational number.

A rational number is a number that can be expressed as the ratio of two integers, and since 7 can be expressed as 7/1, it is a rational number. Therefore, the cube root of 343 is not irrational.

Conclusion

In conclusion, cube root of 343 is is 7 and we can calculate that easily using prime factorization. In this article, we have explored the method prime factorization to calculate the cube root of 343.

Read More,

• Cube Root Calculator
• Cube and Cube Roots
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Cube Root of 343 Solved Examples

Example 1: Simplify this expression: 2 × ∛343 + 10?

Solution:

We know, ∛343 = 7.

2 × ∛343 + 10 = 2(7) + 10 = 14 + 10 = 24

Example 2: The volume of a spherical ball is 343π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 343π in³

⇒ 343π = 4/3 × π × R³

⇒ R³ = 3/4 × 343

⇒ R = ∛(3/4 × 343)

⇒ R = ∛(3/4) × ∛343

⇒ R = 0.90856 × 7 (∵ ∛(3/4) = 0.90856 and ∛343 = 7)

Thus, R is 6.35992 in³.

Example 3: What is the value of ∛343 + ∛(-343)?

Solution:

The cube root of -343 is equal to the negative of the cube root of 343.

i.e. ∛-343 = -∛343

Therefore, ∛343 + ∛(-343) = ∛343 – ∛343 = 0

Example 4: Find the real root of the equation x³ − 343 = 0.

Solution:

x³ − 343 = 0 i.e. x³ = 343

⇒ x = ∛343, x = (-7 + 7√3i)/2 and x = (-7 – 7√3i)/2

Where i is called the imaginary unit and is equal to √-1.

Ignoring imaginary roots,

⇒ x = ∛343

Therefore, the real root of the equation x³ − 343 = 0 is 7.

FAQs on Cube Root of 343

What is the Value of the Cube Root of 343?

We can also write 343 in the form of (7×7×7) hence, ∛343 = ∛(7×7×7) = 7. Hence, the cube root of 343 is 7.

How to Simplify the Cube Root of 343/512?

We know that the cube root of 343 is 7 and the cube root of 512 is 8. Hence, ∛(343/512) = (∛343)/(∛512) = 7/8 = 0.875.

Why is the Cube Root of 343 Rational?

The cube root of 343 can be expressed in the form of p/q, that is, = 7/1, where q ≠ 0. Consequently, ∛343 is rational.

If the Cube Root of 343 is 7, Value of ∛0.343 is?

We will represent √[0.343] in p/q form which is ∛(343/1000) = 7/10 = 0.7. Thus, ∛0.343 = 0.7.

Is 343 a Perfect Cube?

343 has 7 × 7 × 7 as its prime factorization. On combing the prime factors in groups of 3 gives 7. Hence, cube root of 343 is ∛(7 × 7 × 7) = 7 (perfect cube).