Find the value of the following cube root of 686/1024.

To find the cube root of the fraction 686/1024, we can break it down into its components.

Step 1: Simplify the Fraction

First, we simplify the fraction 686/1024. Both numbers can be divided by 2:

• 686 ÷ 2 = 343
• 1024 ÷ 2 = 512

This gives us the simplified fraction:

343/512

Step 2: Find the Cube Roots

Next, we need to find the cube roots of the numerator and the denominator separately:

• The cube root of 343 is 7, since 7 × 7 × 7 = 343.
• The cube root of 512 is 8, since 8 × 8 × 8 = 512.

Step 3: Combine the Results

Now, we can combine the results of the cube roots:

Cube root of 686/1024 = 7/8

Final Answer

The value of the cube root of 686/1024 is 7/8.