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