What is 1/8 sqrt(-72) ?

The solution to 1/8 sqrt(-72) is 3/(2sqrt(2))i

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simplify 1/8 sqrt(-72)

simplify

\frac{1}{8} - 72

\frac{3}{2 2} i

Solution steps

\frac{1}{8} - 72

Prime factorization of

72 : 2^{3} \cdot 3^{2}

= \frac{1}{8} - 2^{3} \cdot 3^{2}

Apply exponent rule:

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

- 2^{3} \cdot 3^{2} = - 2^{2} \cdot 2 \cdot 3^{2}

= \frac{1}{8} - 2^{2} \cdot 2 \cdot 3^{2}

- 2^{2} \cdot 2 \cdot 3^{2} = 2^{2} 2 - 3^{2}

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

Apply radical rule:

a^{2} = a, a \geq 0

2^{2} = 2

= \frac{1}{8} \cdot 22 - 3^{2}

3^{2} = 9

= \frac{1}{8} \cdot 22 - 9

- 9 = 3 i

= \frac{1}{8} \cdot 22 \cdot 3 i

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2 2 \cdot 3}{8} i

Apply rule:

1 \cdot a = a

= \frac{2 2 \cdot 3}{8} i

Cancel

\frac{2 2 \cdot 3}{8} : \frac{3}{2 \cdot 2}

= \frac{3}{2 \cdot 2} i

= \frac{3}{2 2} i

x^{4} + 2 x^{3} + x^{2} - 1

2 x^{2} - 14 x

2 x^{2} - 20 x

\frac{2 x ^{3} y ^{2} n ^{1}}{7 x y ^{2} n ^{3}}

5^{4} \times 5^{- 2}