What is sqrt(2)*\sqrt[3]{2}*\sqrt[4]{2} ?

The solution to sqrt(2)*\sqrt[3]{2}*\sqrt[4]{2} is 2\sqrt[12]{2}

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simplify sqrt(2)\sqrt[3]{2}\sqrt[4]{2}

simplify

Decimal Notation

2.11892 \dots

Solution steps

Apply radical rule:

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

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

Apply radical rule:

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

Apply exponent rule:

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

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

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

\frac{1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{13}{12}

= 2^{\frac{13}{12}}

2^{\frac{13}{12}} = 2^{1 + \frac{1}{12}}

= 2^{1 + \frac{1}{12}}

Apply exponent rule:

x^{a + b} = x^{a} x^{b}

= 2^{1} \cdot 2^{\frac{1}{12}}

Refine

6 \times 6 \times 6

- 3 p^{7} + 3 p^{3}

2 3^{3} + 23

(2 + a)^{2}

9 \frac{3}{8}

What is sqrt(2)*\sqrt[3]{2}*\sqrt[4]{2} ?
The solution to sqrt(2)*\sqrt[3]{2}*\sqrt[4]{2} is 2\sqrt[12]{2}