Simplify This

Algebra Level 1

$\Large \sqrt{2^{\sqrt{{4} x^2}}}$

Which of the following is equal to the above expression where $x\ge 0?$

4^{2x}

2^{2x}

4^{x^2}

2^{x}

2 solutions

Mateus Gomes
Feb 11, 2016

$\Huge \sqrt{\color{#D61F06}2^{\sqrt{\color{#20A900}{4} x^\color{#3D99F6}2}}}=\Huge \sqrt{\color{#D61F06}{2}^{{\color{#20A900}{2x}}}}=(\Huge\color{#D61F06}{2}^{{\color{#20A900}{2x}}})^\frac{1}{2}=(\Huge\color{#D61F06}{2}^{{\color{#20A900}{x}}})$

Diogo Almiro
Feb 13, 2016

$\sqrt{2^{\sqrt{4x^2}}} = \sqrt{2^{2\sqrt{x^2}}} = \sqrt{2^{2|x|}} = 2^{\frac{2}{2}|x|} =2^{|x|} \\ \text{we can ignore the case x<0} \\ 2^x$

Simplify This

2 solutions

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