What to the 3rd power equals 343?

Cube root of 343, represented as 3√343, is a value that returns the original value when multiplied three times by itself. This is the most fundamental definition of a cube root. If an integer is a perfect cube, we can calculate its cube root. We shall get the value of the cube root of 343 in this article by utilizing the prime factorization technique and examples with detailed explanations.

What is the Cube Root?

When a number (x) is multiplied three times, the resulting number is called its cube. As a result, the cube of (x) becomes x3 or x-cubed.

For Example: If we multiply 9 three times, we get 729.

9 x 9 x 9 = 729.. Thus, 9 will be referred to as the cube root of 729.

Symbol of a Cube Root 

The symbol that we use to represent a cube root is the same as that of a square root with the only difference that in a square root, we use the number 2 and in cube root, we use the number 3. The root symbol can also be called a radical symbol. Here is how we represent a cube root:

∛x

What is the Cube Root of 343?

The cube root of 343 is the integer that, when multiplied three times by itself, produces the result 343. Because 343 can be written as 7 7 7. As a result, the cube root of 343 is ∛(7 × 7 × 7) = 7.

Ways to find Cube root

Typically, we apply the prime factorization method to discover the prime factors of a given number. Therefore, if we examine 343 prime factors, we must organize them into groups of three, which provides the cube of factors. Thus, once we have determined the cube of a number's factors, we can apply the cube root, which cancels out the cubes.

Step-by-Step Procedure to find a Prime Factor of 343

Determine the prime factors of 343.

343 equals 7 x 7 x 7

It is self-evident that 343 is a perfect cube. As a result, arrange the 343 components into three pairs and write them as cubes.

343 equals 7x7x7

343 = 73

We will apply the cube root to both sides of the preceding statement to eliminate the word in cubes.

3√343 = 3√(73)

• Thus, the cube root is canceled out in this case by the cube of 7.

As a result, 3√343 = 7

• As a result, the value of 343's cube root is 7.

Examples of Cube Root of 343

Example 1: What is the cube root of 15625?

Solution:

5x5x5x5x5x5 is the cube root of 15625.

= (5x5)x(5x5)x(5x5)

=25x25x25

As a result, 25 equals the cube root of 1562

Example 2: Simplify this expression: 2× 3√343+ 10?

Solution:

We know, 3√343 = 7.

Now, substitute this into the expression.

2×3√343 + 10 = 2(7) + 10

2×3√343 + 10 = 14+10 = 24.

=2×3√343 + 10 = 24.

Example 3: What can the smallest integer be divided by 73002 to form a perfect cube?

Solution:

73002 has a prime factorization of 23 x 23 x 23 x 2 x 3.

There is already a set of three 23s here, but only 2 and 3 remain. Thus, by dividing the number by 6, we may obtain a perfect cube.

So you want to know what 343 to the 3rd power is do you? In this article we'll explain exactly how to perform the mathematical operation called "the exponentiation of 343 to the power of 3". That might sound fancy, but we'll explain this with no jargon! Let's do it.

What is an Exponentiation?

Let's get our terms nailed down first and then we can see how to work out what 343 to the 3rd power is.

When we talk about exponentiation all we really mean is that we are multiplying a number which we call the base (in this case 343) by itself a certain number of times. The exponent is the number of times to multiply 343 by itself, which in this case is 3 times.

There are a number of ways this can be expressed and the most common ways you'll see 343 to the 3rd shown are:

So basically, you'll either see the exponent using superscript (to make it smaller and slightly above the base number) or you'll use the caret symbol (^) to signify the exponent. The caret is useful in situations where you might not want or need to use superscript.

So we mentioned that exponentation means multiplying the base number by itself for the exponent number of times. Let's look at that a little more visually:

343 to the 3rd Power = 343 x ... x 343 (3 times)

So What is the Answer?

Now that we've explained the theory behind this, let's crunch the numbers and figure out what 343 to the 3rd power is:

343 to the power of 3 = 3433 = 40,353,607

Why do we use exponentiations like 3433 anyway? Well, it makes it much easier for us to write multiplications and conduct mathematical operations with both large and small numbers when you are working with numbers with a lot of trailing zeroes or a lot of decimal places.

Hopefully this article has helped you to understand how and why we use exponentiation and given you the answer you were originally looking for. Now that you know what 343 to the 3rd power is you can continue on your merry way.

Feel free to share this article with a friend if you think it will help them, or continue on down to find some more examples.

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