Answer:
To find the square root of \(18x^7y^6\) i.e, \(\sqrt{18x^7y^6}\)
Using radical rules:
\(\sqrt[n]{a^n} = a\)
\((a^m)^{\frac{1}{n}} = a^{\frac{m}{n}}\)
we can write:
\(18 = 3 \cdot 3 \cdot 2 = 3^2 \cdot 2\)
\(x^7 = x^6 \cdot x\)
then;
\(\sqrt{18x^7y^6}\) = \(\sqrt{3^2 \cdot 2 \cdot x^6 \cdot x \cdot y^6}\)
Apply the rules we have;
\(3 \cdot x^3 \cdot y^3 \cdot \sqrt{2x}\)
or
\(3x^3y^3\sqrt{2x}\)
therefore, \(3x^3y^3\sqrt{2x}\) is equal to \(\sqrt{18x^7y^6}\)
