What is sqrt(\sqrt[5]{(32)(243))} ?

The solution to sqrt(\sqrt[5]{(32)(243))} is square root of 6

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simplify sqrt(\sqrt[5]{(32)(243))}

simplify

6

Decimal Notation

2.44948 \dots

Solution steps

Apply radical rule:

= ((32 \cdot 243)^{\frac{1}{5}})^{\frac{1}{2}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= (32 \cdot 243)^{\frac{1}{5} \cdot \frac{1}{2}}

\frac{1}{5} \cdot \frac{1}{2} = \frac{1}{10}

= (32 \cdot 243)^{\frac{1}{10}}

Multiply the numbers:

32 \cdot 243 = 7776

Factor the number:

7776 = 6^{5}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 6

t^{3} e^{- a t}

(a + b + x + y) (a^{2} b^{2})

4 t (4 t^{3})

999.9999800000000 \dots (4 \cdot 1 0^{- 3})

What is sqrt(\sqrt[5]{(32)(243))} ?
The solution to sqrt(\sqrt[5]{(32)(243))} is square root of 6