What is (sqrt(200))/8 ?

The solution to (sqrt(200))/8 is 5/(2sqrt(2))

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simplify (sqrt(200))/8

simplify

\frac{200}{8}

\frac{5}{2 2}

Solution steps

\frac{200}{8}

Factor

200 : 250

= \frac{2 50}{8}

Factor the number:

8 = 2^{3}

= \frac{2 50}{2 ^{3}}

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

= \frac{50}{2 ^{2}}

Factor

50 : 2 \cdot 5

= \frac{2 \cdot 5}{2 ^{2}}

Apply exponent rule:

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

2^{2} = 2 \cdot 2

= \frac{2 \cdot 5}{2 \cdot 2}

Apply radical rule:

a = a a

2 = 22

= \frac{2 \cdot 5}{2 2 \cdot 2}

Cancel the common factor:

2

= \frac{5}{2 \cdot 2}

= \frac{5}{2 2}

6 \cdot 25

\frac{( \frac{64}{- 27} )}{( \frac{- 12}{7} )}

\frac{1}{2} (x^{2} + 1) - \frac{3}{2} (x^{2} - 1)

2 x^{2} + 6 x + 8 x^{3} - 12 x^{4}

5 14 z^{2} \cdot 4 21 z^{3}