Answer :

GinnyAnswer
To find the cube root of each given expression, let's solve them step-by-step.

### Problem 6: Finding the cube root of [tex]\( 216 \times 125000 \)[/tex]

1. Calculate the product:
[tex]\[ 216 \times 125000 = 27000000 \][/tex]

2. Identify the number to find the cube root of:
[tex]\[ 27000000 \][/tex]

3. Find the cube root of [tex]\( 27000000 \)[/tex]:
[tex]\[ \sqrt[3]{27000000} \approx 300 \][/tex]

Thus, the cube root of [tex]\( 27000000 \)[/tex] is approximately [tex]\( 300 \)[/tex].

### Problem 7: Finding the cube root of [tex]\( -343 \times 64 \)[/tex]

1. Calculate the product:
[tex]\[ -343 \times 64 = -21952 \][/tex]

2. Identify the number to find the cube root of:
[tex]\[ -21952 \][/tex]

3. Finding cube roots of negative numbers can result in complex numbers when the root isn't an exact real number. In our case:
[tex]\[ \sqrt[3]{-21952} \approx 14 + 24.25i \][/tex]

Thus, the cube root of [tex]\( -21952 \)[/tex] is approximately [tex]\( 14 + 24.25i \)[/tex].

### Summary:
- Cube root of [tex]\( 216 \times 125000 \)[/tex] is approximately [tex]\( 300 \)[/tex].
- Cube root of [tex]\( -343 \times 64 \)[/tex] is approximately [tex]\( 14 + 24.25i \)[/tex].

These detailed steps outline how the products were first calculated and then their cube roots were determined.

Answer:

6. 300

7. 28

Step-by-step explanation:

What is a cubed root?

The cubed root is a number that needs to be multiplied three times to get the original. Using the equation [tex]\sqrt[3]{y} =x[/tex] can help you find the cubed root. Check your answer using this equation [tex]x^{3} =y[/tex].

For example:

  • [tex]\sqrt[3]{64} =4[/tex], [tex]4^{3} =64[/tex], 4×4×4=64

With this in mind, first find the product of the two multiplied values:

  • 216 × 125000= 27000000
  • -343 × 64= 21952

Next, write the cubed root function for each and use a scientific calculator to find the answers:

  • [tex]\sqrt[3]{27,000,000}[/tex] = 300
  • [tex]\sqrt[3]{21952}[/tex] = 28

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