Cubes and Cube Roots

Calculate the value of $12^3$.

Express $(\frac{1}{10})^3$ as a decimal.

Determine the unit digit of $79^3$.

Find the value of $13^3$.

What is the value of $\sqrt{1^3 + 2^3 + 3^3 + 4^3 + 5^3 + 6^3}$?

How many perfect cubes are there between $1$ and $500$ (inclusive)?

The value of $\sqrt[3]{0.000008}$ is:

Evaluate the value of the following expression using the properties of cube numbers: $\sqrt[3]{333^3 + 444^3 + 555^3}$.

If the cube of a number $x$ is $k$, what is the cube of $\frac{2x}{3}$ in terms of $k$?

Find the value of $n$ if $1^3 + 2^3 + ... + n^3 = 3025$.

Find the cube root of $21 \times 21 \times 21$ using the prime factorisation method.

If $a = 2$ and $b = 5$, find the value of $\sqrt[3]{a^3 \times b^3}$ using prime factorisation.

What is the cube root of $10^6$ based on prime factorisation triplets?

Find the value of $\sqrt[3]{2 \times 2 \times 2 \times 6 \times 6 \times 6}$.

Determine the value of $\sqrt[3]{0.064 \times 125}$ using prime factors.

Calculate $\sqrt[3]{3375 \times 8}$ using the prime factorisation method.

Find the smallest number to multiply $128$ to get a perfect cube.

Evaluate $\sqrt[3]{2^{12} \times 3^3 \times 5^3}$ by prime factorisation.

Find the cube root of $7^3 \times 11^3 \times 2^6$ by resolving the product.

Find the cube root of $2^9 \times 3^3 \times 5^6$ using the laws of exponents and prime factorisation logic.