Question

The volume of a cube is 1,953,125 centimeters what is the length of the sides

Answer 1

125 cm

Explanation:

The formula of a volume of a cube:

`V=a^3`

a - edge of cube

We have V = 1,953,125 cm³. Substitute:

`a^3=1,953,125\to a=\sqrt[3]{1,953,125}\\\\\begin{array}c1,953,125&5\\390,625&5\\78,125&5\\15,625&5\\3,125&5\\625&5\\125&5\\25&5\\5&5\\1\end{array}\\\\1,953,125=5^3\cdot5^3\cdot5^3\\\\\sqrt[3]{1,953,125}=\sqrt[3]{5^3\cdot5^3\cdot5^3}\qquad\text{use}\ \sqrt[3]{ab}=\sqrt[3]a\cdot\sqrt[3]b\\\\=\sqrt[3]{5^3}\cdot\sqrt[3]{5^3}\cdot\sqrt[3]{5^3}\qquad\text{use}\ \sqrt[3]{a^3}=a\\\\=5\cdot5\cdot5=125`