Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$5/ \sqrt{ 10-3 \times } \times 5/ \sqrt{ 10+3 }$$

Answer

(25*sqrt(13))/(13*sqrt(10-3*))

Solution


Simplify  \(10+3\)  to  \(13\).
\[\frac{5}{\sqrt{10-3}}\times \frac{5}{\sqrt{13}}\]
Rationalize the denominator: \(\frac{5}{\sqrt{10-3}} \cdot \frac{\sqrt{10-3}}{\sqrt{10-3}}=\frac{5\sqrt{10-3}}{10-3}\).
\[\frac{5\sqrt{10-3}}{10-3}\times \frac{5}{\sqrt{13}}\]
Rationalize the denominator: \(\frac{5\sqrt{10-3}}{10-3}\times \frac{5}{\sqrt{13}} \cdot \frac{\sqrt{13}}{\sqrt{13}}=\frac{5\sqrt{10-3}\times 5\sqrt{13}}{(10-3)\times 13}\).
\[\frac{5\sqrt{10-3}\times 5\sqrt{13}}{(10-3)\times 13}\]
Simplify  \(5\sqrt{10-3}\times 5\sqrt{13}\)  to  \(25\sqrt{10-3}\sqrt{13}\).
\[\frac{25\sqrt{10-3}\sqrt{13}}{(10-3)\times 13}\]
Simplify.
\[\frac{25\sqrt{13}}{13\sqrt{10-3}}\]
Rationalize the denominator: \(\frac{25\sqrt{13}}{13\sqrt{10-3}} \cdot \frac{\sqrt{10-3}}{\sqrt{10-3}}=\frac{25\sqrt{13}\sqrt{10-3}}{13(10-3)}\).
\[\frac{25\sqrt{13}\sqrt{10-3}}{13(10-3)}\]
Simplify.
\[\frac{25\sqrt{13}}{13\sqrt{10-3}}\]
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