What is 1/2 sqrt(8) ?

The solution to 1/2 sqrt(8) is square root of 2

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simplify 1/2 sqrt(8)

simplify

\frac{1}{2} 8

2

Solution steps

\frac{1}{2} 8

Prime factorization of

8 : 2^{3}

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

Apply exponent rule:

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

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

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

Apply radical rule:

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

2^{2} \cdot 2 = 2^{2} 2

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

Apply radical rule:

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

2^{2} = 2

= \frac{1}{2} \cdot 22

Convert

2

to fraction

: \frac{2}{1}

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

Cross-cancel common factor:

2

= 1 \cdot 2

Apply rule:

1 \cdot a = a

= 2

\frac{3}{7} \cdot 5

- 5^{- 4}

[(\frac{1}{2} x^{- 2})^{3} (4 x y^{- 1})^{2}]^{2}