Question

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

Answer 1

`\sqrt{180x ^{9y ^(16) } }`

Apply radical rule :


`\sqrt[n]{ab} = \sqrt[n]{a} \sqrt[n]{b}`


`√(180) \sqrt{x ^{9y^(16) } }`

Break the number to its primes :
`180 : 2^2*3^2*5`


`√(2^2*3^2*5)`

Apply radical rule :


`\sqrt[n]{ab} = \sqrt[n]{a} \sqrt[n]{b}`


`√(5) √(2^2) √(3^2)`

Apply radical rule :


`\sqrt[n]{a^n} =a`


`√(2^2) =2`


`2* √(5) √(3^2)`

Apply radical rule :


`\sqrt[n]{a^n} =a`


`√(3^2) =3`


`= 2*3* √(5)`

Refine:


`√(5) *6`


`√(5) *6 \sqrt{x ^{9y ^(16) } }`

Apply radical rule :


`\sqrt[n]{a^m} = a (m)/(n)`


`\sqrt{x ^{9y ^(16) } } = x (9y ^(16) )/(2)`


`= √(5) *6x (9y ^(16) )/(2)`

hope this helps!