Evaluate 15 - 10 - 20 - 40 - 5 - 80

15 √( 10 ) +√( 20 ) +√( 40 ) √( 5 ) √( 80 ) #160; =15√(10)+2√(5)+2√(10) √(5) 4√(5) =153√(10) 3√(5) =5√(10) √(5) =√(5)(√(2) 1) ...

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Number Theory: Interesting Results

Evaluate 15...

Question

Evaluate $\frac{15}{\sqrt{10} + \sqrt{20} + \sqrt{40} - \sqrt{5} - \sqrt{80}}$

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Solution

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Evaluate $\frac{15}{\sqrt{10} + \sqrt{20} + \sqrt{40} - \sqrt{5} - \sqrt{80}}$ , it us given that $\sqrt{5} = 2.236$ and $\sqrt{10} = 3.162$

\frac{15}{\sqrt{10} + \sqrt{20} + \sqrt{40} - \sqrt{5} - \sqrt{80}}

\sqrt{5} = 2.236

\sqrt{10} = 3.162

\frac{15}{\sqrt{10} + \sqrt{20} + \sqrt{40} - \sqrt{5} - \sqrt{80}}

\sqrt{5} = 2.236 and \sqrt{10} = 3.162

\begin{array}{rcl} \frac{15}{\sqrt{10} + \sqrt{20} + \sqrt{40} - \sqrt{5} - \sqrt{80}} & = & \frac{15}{\sqrt{10} + 2 \sqrt{5} + 2 \sqrt{10} - \sqrt{5} - 4 \sqrt{5}} \\ = & \frac{15}{3 \sqrt{10} - 3 \sqrt{5}} = \frac{5}{\sqrt{10} - \sqrt{5}} \end{array}

X	$0 - 5$	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$
F	$40$	$80$	$20$	$16$	$20$

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