1. Find the cube root of 8.
2. Find the cube root of 27.
3. Find the cube root of 64.
4. Find the cube root of 125.
5. Find the cube root of 216.
6. Find the cube root of 343.
7. Find the cube root of 512.
8. Find the cube root of 729.
9. Find the cube root of 1000.
10. Write the cube root of 64 in radical form and find its value.
1. Cube root of 8: We look for a number that, when multiplied by itself three times, equals 8. Since $2 \times 2 \times 2 = 8$, the answer is 2.
2. Cube root of 27: Breaking 27 into its prime factors gives us $3 \times 3 \times 3$. Therefore, the cube root is 3.
3. Cube root of 64: We can see that $4 \times 4 = 16$, and $16 \times 4 = 64$. Since 4 cubed is 64, the root is 4.
4. Cube root of 125: Any number ending in 5 is likely a multiple of 5. Calculating $5 \times 5 \times 5$ gives us exactly 125, so the root is 5.
5. Cube root of 216: This can be factored into $6 \times 6 \times 6$. Because 6 multiplied by itself three times is 216, the root is 6.
6. Cube root of 343: This is a unique one to memorize. Testing 7, we find that $7 \times 7 = 49$, and $49 \times 7 = 343$. The answer is 7.
7. Cube root of 512: Following the pattern of even numbers, we find $8 \times 8 \times 8 = 512$. Thus, the cube root is 8.
8. Cube root of 729: Since $9 \times 9 = 81$ and $81 \times 9 = 729$, the cube root is 9.
9. Cube root of 1000: For powers of 10, you can count the zeros. Since there are three zeros, $10 \times 10 \times 10 = 1000$. The root is 10.
10. Radical form of 64: To write this in radical form, we use the radical symbol with an index of 3: $\sqrt[3]{64}$. As solved in problem 3, the value is 4.