What is sqrt(4\sqrt{3)} ?

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

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simplify sqrt(4\sqrt{3)}

simplify

43

Decimal Notation

2.63214 \dots

Solution steps

43

Apply radical rule:

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

43 = 43

= 43

4 = 2

= 23

Apply radical rule:

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

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

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

Apply radical rule:

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

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

= 2 (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}}

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

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

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

Apply exponent rule:

\frac{a ^{- 2} + b ^{- 1}}{a ^{- 1} - 5 b ^{- 3}}

x^{2} + y^{2}

\frac{\frac{1}{a} - \frac{9}{a ^{2}} + \frac{20}{a ^{3}}}{\frac{16}{a} - a}