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Cube Root of 343 is 7. It is represented as 3√343. Cube root of 343 is the value that returns the original value when we multiply it three times by itself. It means when we multiply the cube root of 343, i.e. 7 thrice by itself, we will get 343 only. The cube root of 343 is the real solution of the equation x3 = 343. Since the cube root of 347 is 7, which is a whole number, thus, 343 is a perfect cube. In radical form, the cube root of 343 is expressed as ∛343 while it is expressed as (343)⅓ or (343)0.33 in the exponent form.
Read More: NCERT Solutions for Class 8 Mathematics Cube and Cube Roots
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Key Terms: Cube Root of 343, Perfect Cube, Prime Factorization, Cube Root, Whole Number, Rational Number, Radical Form, Cube
What is Cube Root of 343?
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Cube Root of 343 is the number that gives the product as 343 on multiplication with itself three times. The cube root of 343 is represented as 3√343. The value of the cube root of 343 is 7.
3√343 = 3√(Number × Number × Number)
3√343 = 3√(7 × 7 × 7) = 7
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| Cube and Cube Roots | Square Roots | Cube Root 1 to 20 |
How to Find Cube Root of 343?
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Prime Factorisation is usually used to find the prime factors of the given number. Thus, in order to evaluate the prime factors of 343, we need to pair them in a group of three that would give us the cube of factors. Once the cube of factors of a number is found, we can put the cube root, which gets canceled with the cubes.
Cube Root of 343
Here is a step-by-step procedure to calculate the cube root of 343:
Step 1: Find out the prime factors of 343 using prime factorization.
343 = 7 × 7 × 7
Step 2: We can clearly see that 343 is a perfect cube. Thus, group the factors of 343 in a pair of three and write in the form of cubes.
343 = 7 × 7 × 7
343 = 73
Step 3: Apply cube root to both sides of the above expression to take out the term in cubes.
3√343 = 3√(73)
The cube root is canceled by the cube of 7. Thus,
3√343 = 7
Therefore, the value of the cube root of 343 is 7.
Cube Root of 343
Is Cube Root of 343 Irrational?
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No. The cube root of 342 is not irrational, since the cube root of 343 can be represented in the form of p/q.
∛343 = ∛(7 × 7 × 7)
We can represent the cube root of 343 which is 7 in p/q form like 7/1. Therefore, the value of cube root of 343 is an integer which makes it rational.
Read More: Cubes and Cube Roots MCQs
Solved Examples on Cube Root of 343
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Here are a few solved examples on cube root of 343:
Example 1: Solve the expression: 2 × 3√343+ 10
Solution: Given expression is 2 × 3√343 + 10
Cube root of 343 is 7, i.e. 3√343 = 7
Substitute the value in the given expression,
2 × 3√343 + 10 = 2(7) + 10
2 × 3√343 + 10 = 14+10 = 24.
Thus, the value of 2 × 3√343 + 10 is 24.
Example 2: Calculate the value of k if k × 3√343= 35.
Solution: We are given the equation
k × 3√343 = 35
Cube root of 343 is 7.
Substitute value in the given expression,
k (7) = 35
k = 35/7
k = 5
Thus, the value of k is 5.
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| Square Roots | Factoring Formula | Root Mean Square |
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Cube Root of Perfect Cubes
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Cube root of a few numbers has been provided below. The following numbers are perfect cubes. Perfect cubes are the numbers that are obtained by multiplying the same integer three times. One must memorize the value of the cube roots of the given numbers for faster calculations:
| Number (n) | Cube Root of Number (3√n) |
|---|---|
| 1 | 1 |
| 8 | 2 |
| 27 | 3 |
| 64 | 4 |
| 125 | 5 |
| 216 | 6 |
| 343 | 7 |
| 512 | 8 |
| 729 | 9 |
| 1000 | 10 |
Things to Remember
- Cube Root of 343 refers to the value that gives the product as 343 on multiplication with itself thrice.
- Cube Root of 343 is 7.
- Cube root of 343 can be expressed as 3√343 = 3√(7×7×7) = 7.
- The radical form of the cube root of 343 is ∛343 while the exponential form is (343)⅓ or (343)0.33.
- 343 is a perfect cube which means the cube root of 343, i.e. 7, is a whole number.
Sample Questions
Ques. What will be the radius of the ball if the volume of a spherical ball is 343π in3? (3 Marks)
Ans. It is given that,
Volume of Spherical Ball = 343π in3
= 4/3 × π × R3
= R3 = 3/4 × 343
= R = ∛(3/4 × 343) = ∛(3/4) × ∛343 = 0.90856 × 7 (Since, ∛(3/4) = 0.90856 and ∛343 = 7)
= R = 6.35992 in3
Thus, the radius of the spherical ball is 6.35992 in3
Ques. Calculate the value of ∛343 + ∛(-343). (2 Marks)
Ans. Cube root of -343 is equal to the negative of the cube root of 343.
Thus,
∛-343 = -∛343
Therefore,
∛343 + ∛(-343) = ∛343 - ∛343 = 0
Ques. Calculate the real root of the equation x3 − 343 = 0. (3 Marks)
Ans. It is given that,
x3 − 343 = 0
Thus, x3 = 343
Solving for x, we get
x = ∛343, x = ∛343 × (-1 + √3i))/2 and x = ∛343 × (-1 - √3i))/2
Where i refers to the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛343
Thus, the real root of the equation x3 − 343 = 0 is for x = ∛343 = 7.
Ques. What is the value of cube root of 343? (1 Mark)
Ans. The value of the cube root of 343 is 7.
∛343 = 7
Ques. Is 343 a perfect cube? (1 Mark)
Ans. Yes, 343 is a perfect cube as it can be expressed as the product of the whole number 7 thrice by itself.
Ques. Is the cube root of 343 rational? (2 Marks)
Ans. Yes, the cube root of 343 is rational. We know that the cube root of 343 is 7 which is a whole number and can be written in the form of p/q. Thus, the cube root of 343 is rational.
Ques. Write the value of the cube of cube root of 343. (2 Marks)
Ans. The value of cube of cube root of 343 will be
(3√343)3 = 73 = 343
Thus, the value of the cube of cube root of 343 is 343 itself.
Ques. Find the value of 10 plus the cube root of 343. (1 Mark)
Ans. We know that the value of the cube root of 343 is 7.
Thus, 10 + 3√343 = 10+7 = 17
Ques. What is the value of Cube Root of 343/512? (2 Marks)
Ans. We know that the cube root of 343 is 7. Also, the cube root of 512 is 8.
Therefore,
∛(343/512) = (∛343)/(∛512)
= 7/8 = 0.875
Thus, the value of Cube Root of 343/512 is 0.875.
Ques. Find the value of 9 Plus 8 Cube Root 343. (2 Marks)
Ans. We know that the value of ∛343 is 7.
Thus,
9 + 8 × ∛343
= 9 + 8 × 7
= 65.
Thus, the value of 9 plus 8 cube root 343 is 65.
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