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Popular >

simplify sqrt(16^{3/4)}

Solution

simplify

1 6^{\frac{3}{4}}

Solution

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

+1

Decimal Notation

2.82842 \dots

Solution steps

1 6^{\frac{3}{4}}

Apply radical rule:

1 6^{\frac{3}{4}} = 1 6^{\frac{\frac{3}{4}}{2}}

= 1 6^{\frac{\frac{3}{4}}{2}}

\frac{\frac{3}{4}}{2} = \frac{3}{8}

= 1 6^{\frac{3}{8}}

1 6^{\frac{3}{8}} = 2^{\frac{3}{2}}

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

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

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

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

Apply exponent rule:

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

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

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

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

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

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

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

Apply exponent rule:

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

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

Refine

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

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Frequently Asked Questions (FAQ)

What is sqrt(16^{3/4)} ?
The solution to sqrt(16^{3/4)} is 2*2^{1/2}