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Popular >

simplify sqrt(\sqrt{3e^8)}

Solution

simplify

3 e^{8}

Solution

+1

Decimal Notation

9.72454 \dots

Solution steps

3 e^{8}

Apply radical rule:

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

= ((3 e^{8})^{\frac{1}{2}})^{\frac{1}{2}}

Apply exponent rule:

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

= (3 e^{8})^{\frac{1}{2} \cdot \frac{1}{2}}

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

= (3 e^{8})^{\frac{1}{4}}

Apply radical rule:

assuming

a \geq 0, b \geq 0

Apply exponent rule:

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

e^{8} = e^{2 \cdot 4} = (e^{2})^{4}

Apply radical rule:

assuming

a \geq 0

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Frequently Asked Questions (FAQ)

What is sqrt(\sqrt{3e^8)} ?
The solution to sqrt(\sqrt{3e^8)} is \sqrt[4]{3}e^2