Question

Root under 400-256 divided by root 400- root250.

Answer 1

Dear student,
Here is the solution of your asked query:

$$\begin{gathered} \mathrm{Taking}\mathrm{the}\mathrm{given}\mathrm{expression}\mathrm{as}\frac{\sqrt{400}{\displaystyle -}{\displaystyle \sqrt{256}}}{\sqrt{400}{\displaystyle -}{\displaystyle \sqrt{250}}} \\ =\frac{\sqrt{20\times 20}{\displaystyle -}{\displaystyle \sqrt{16\times 16}}}{\sqrt{20\times 20}{\displaystyle -}{\displaystyle \sqrt{5\times 5\times 10}}} \\ =\frac{20-16}{20-5\sqrt{10}} \\ =\frac{4}{20-5\sqrt{10}} \\ =\frac{{\displaystyle 4}}{{\displaystyle 20-5\sqrt{10}}}\times \frac{20+5\sqrt{10}}{20+5\sqrt{10}}\{\mathrm{rationalising}\mathrm{the}\mathrm{denominator}\} \\ =\frac{80+20\sqrt{10}}{{20}^2-{\left(5\sqrt{10}\right)}^2} \\ =\frac{80+20\sqrt{10}}{400-250} \\ =\frac{80+20\sqrt{10}}{150} \end{gathered}$$
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