What is the square root of 180x^9y^16 in simplest form?

Answers

6/9 i need more characters in my answer

the 3rd option is right

step-by-step explanation:

\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!
\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!


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