What is 0.08*30*(1+0.0001*30)^{-1/2} ?

The solution to 0.08*30*(1+0.0001*30)^{-1/2} is (10^{1/2}*24)/(1003^{1/2)}

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simplify 0.0830(1+0.0001*30)^{-1/2}

simplify

0.08 \cdot 30 \cdot (1 + 0.0001 \cdot 30)^{- \frac{1}{2}}

\frac{1 0 ^{\frac{1}{2}} \cdot 24}{100 3 ^{\frac{1}{2}}}

Decimal Notation

2.39640 \dots

Solution steps

0.08 \cdot 30 (1 + 0.0001 \cdot 30)^{- \frac{1}{2}}

Multiply the numbers:

0.08 \cdot 30 = 2.4

= 2.4 (1 + 0.0001 \cdot 30)^{- \frac{1}{2}}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

(1 + 0.0001 \cdot 30)^{- \frac{1}{2}} = \frac{1}{( 1 + 0.0001 \cdot 30 ) ^{\frac{1}{2}}}

= 2.4 \cdot \frac{1}{( 1 + 0.0001 \cdot 30 ) ^{\frac{1}{2}}}

(1 + 0.0001 \cdot 30)^{\frac{1}{2}} = \frac{100 3 ^{\frac{1}{2}}}{10 \cdot 1 0 ^{\frac{1}{2}}}

= 2.4 \cdot \frac{1}{\frac{100 3 ^{\frac{1}{2}}}{10 \cdot 1 0 ^{\frac{1}{2}}}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= 2.4 \cdot \frac{10 \cdot 1 0 ^{\frac{1}{2}}}{100 3 ^{\frac{1}{2}}}

2.4 \cdot \frac{10 \cdot 1 0 ^{\frac{1}{2}}}{100 3 ^{\frac{1}{2}}} = \frac{1 0 ^{\frac{1}{2}} \cdot 24}{100 3 ^{\frac{1}{2}}}

= \frac{1 0 ^{\frac{1}{2}} \cdot 24}{100 3 ^{\frac{1}{2}}}

1 - x^{2} \cdot x^{2} - 1

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

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

2 (214)

(a + 3) \cdot (a - 3)

What is 0.08*30*(1+0.0001*30)^{-1/2} ?
The solution to 0.08*30*(1+0.0001*30)^{-1/2} is (10^{1/2}*24)/(1003^{1/2)}