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Popular >

simplify sqrt(3*\sqrt{3)}

Solution

simplify

3 \cdot 3

Solution

4 3^{3}

+1

Decimal

2.27950 \dots

Solution steps

33

Apply radical rule:

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

33 = 33

= 33

3 = 43

= 343

Apply radical rule:

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

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

= 3^{\frac{1}{2}} 43

Apply radical rule:

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

43 = 3^{\frac{1}{4}}

= 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}}

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

= 4 3^{3}

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Frequently Asked Questions (FAQ)

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