What is sqrt(\sqrt{\sqrt{729)}} ?

The solution to sqrt(\sqrt{\sqrt{729)}} is \sqrt[4]{3^3}

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simplify sqrt(\sqrt{\sqrt{729)}}

simplify

729

Decimal Notation

2.27950 \dots

Solution steps

729

729 = 33

= 33

Apply radical rule:

ab = a b, a \geq 0, b \geq 0

33 = 33

= 33

Apply radical rule:

a = a^{\frac{1}{2}}

3 = 3^{\frac{1}{2}}

Apply radical rule:

= 3^{\frac{1}{2}} \cdot 3^{\frac{1}{4}}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

3^{\frac{1}{2}} \cdot 3^{\frac{1}{4}} = 3^{\frac{1}{2} + \frac{1}{4}}

= 3^{\frac{1}{2} + \frac{1}{4}}

\frac{1}{2} + \frac{1}{4} = \frac{3}{4}

= 3^{\frac{3}{4}}

x^{2} (2 x + 5)^{2}

8 e^{- 3}

3.009 \cdot 1 0^{- 5}

e^{- 2 x} (e^{4 x})

What is sqrt(\sqrt{\sqrt{729)}} ?
The solution to sqrt(\sqrt{\sqrt{729)}} is \sqrt[4]{3^3}