What is sqrt(\sqrt{243)} ?

The solution to sqrt(\sqrt{243)} is 3\sqrt[4]{3}

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simplify sqrt(\sqrt{243)}

simplify

243

Decimal Notation

3.94822 \dots

Solution steps

243

243 = 93

= 93

Apply radical rule:

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

93 = 93

= 93

9 = 3

= 33

Apply radical rule:

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

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

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

Apply radical rule:

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

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

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

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

(3^{\frac{1}{2}})^{\frac{1}{2}} = 3^{\frac{1}{2} \cdot \frac{1}{2}}

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

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

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

Apply exponent rule:

- 218 + 50

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