Question

Simplify: √(1/4) + 2√(.0001) - (1000)^-2/3 is-​

Answer 1

Step-by-step explanation:

$\textsf{Hey Thomas!!}$

$\bf \underline{Solution-}$

$\textsf{We have,}$

$\sf{\sqrt { \frac { 1 } { 4 } } + \sqrt [ 2 ] { ( .0001 ) } - ( 1000 ) ^ { - 2 /3 }}$

$\sf{\Rightarrow{ \: \frac{1}{2} + 0.1 - \left \{ \bigg( \frac{1}{10} \bigg) ^{3} \right \} ^{2/3} }}$

$\sf{\Rightarrow{ \: \frac{1}{2} + 0.1 - \bigg( \frac{1}{10} \bigg) ^{ \cancel3 \times 2/ \cancel3} }}$

$\sf{\Rightarrow{ \: \frac{1}{2} + 0.1 - \bigg( \frac{1}{10} \bigg) ^{ 2} }}$

$\sf{\Rightarrow{ \: \frac{1}{2} +0.1 - (0.1 {)}^{2} }}$

$\sf{\Rightarrow{ \: \frac{1}{2} + \cancel{0.1 }- \cancel{ 0.1}}}$

$\sf{\Rightarrow{ \: \frac{1}{2}}}$

$\bf \underline{Answer-}$

$\textsf{Hence after simplifying, we get the value of:}$

$\underline{ \boxed{ \sf{\sqrt { \frac { 1 } { 4 } } + \sqrt [ 2 ] { ( .0001 ) } - ( 1000 ) ^ { - 2 /3 }} \: is \: \frac{1}{2}}.}$