\(\sqrt{180x ^{9y ^{16} } }\)
Apply radical rule :
\(\sqrt[n]{ab} = \sqrt[n]{a} \sqrt[n]{b}\)
\(\sqrt{180} \sqrt{x ^{9y^{16} } }\)
Break the number to its primes : \(180 : 2^2*3^2*5\)
\(\sqrt{2^2*3^2*5}\)
Apply radical rule :
\(\sqrt[n]{ab} = \sqrt[n]{a} \sqrt[n]{b}\)
\(\sqrt{5} \sqrt{2^2} \sqrt{3^2}\)
Apply radical rule :
\(\sqrt[n]{a^n} =a\)
\(\sqrt{2^2} =2\)
\(2* \sqrt{5} \sqrt{3^2}\)
Apply radical rule :
\(\sqrt[n]{a^n} =a\)
\(\sqrt{3^2} =3\)
\(= 2*3* \sqrt{5}\)
Refine:
\(\sqrt{5} *6\)
\(\sqrt{5} *6 \sqrt{x ^{9y ^{16} } }\)
Apply radical rule :
\(\sqrt[n]{a^m} = a \frac{m}{n}\)
\(\sqrt{x ^{9y ^{16} } } = x \frac{9y ^{16} }{2}\)
\(= \sqrt{5} *6x \frac{9y ^{16} }{2}\)
hope this helps!
