Confusing Square Root

Algebra Level 2

$\Huge \sqrt{\color{#D61F06}9^{\color{#20A900}{16} \color{#3D99F6}{x^2}}}$

Which of the following is equal to the above expression?

\Large{ 3 }^{ 4{ x } }

\Large{ 3 }^{ 8{ x }^{ 2 } }

\Large{ 9 }^{ 4{ x } }

\Large { 9 }^{ 8{ x }^{ 2 } }

2 solutions

Julian Uy
Jan 7, 2015

By Rules of Exponents , $\large \sqrt{a^x} = \left|a^{x/2}\right|$ . So,

$\Large \sqrt { { 9 }^{ { 16 }x^{ 2 } } } ={ 9 }^{ (16{ x }^{ 2 })/2 }={ 9 }^{ 8{ x }^{ 2 } }.$

Same solution as I did

Syed Baqir - 5 years, 5 months ago

do not agree

Ben Hunter - 5 years, 5 months ago

That's not correct

Jarric Weber - 5 years, 1 month ago

It should be 9^8x : (9^16x^2) ^.5 = 9^8x not 9^8x^2

Jane Dornbusch - 5 years, 4 months ago

It's only 8x^2. To get 8x you would be halving the coefficient but square rooting the x part.

Thomas Morris - 5 years, 1 month ago

nice question

Arun Garg - 5 years, 1 month ago

Cooooooool

Abhishek Kushwaha - 4 years, 11 months ago

Paola Ramírez
Jan 14, 2015

$\sqrt{9^{16x^2}}=\sqrt{9^{8x^2}\times9^{8x^2}}=9^{8x^2}$

best way, so far.

Pedro Thomasi - 4 years, 12 months ago

neat; many years since I read this

Brian Maire - 5 years ago

Nice solution

Avanish Anand - 5 years, 5 months ago

9*9=81 so how's this possible

Tajrin Kashem - 4 years, 11 months ago