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The simplified form is \( \frac{10\sqrt{7}+5\sqrt{5}}{23} \).
Solución
Calculate or simplify the expression \( \frac{5}{2 \sqrt{7}-\sqrt{5}} \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{5}{2\sqrt{7}-\sqrt{5}}\)
- step1: Multiply by the Conjugate:
\(\frac{5\left(2\sqrt{7}+\sqrt{5}\right)}{\left(2\sqrt{7}-\sqrt{5}\right)\left(2\sqrt{7}+\sqrt{5}\right)}\)
- step2: Multiply the numbers:
\(\frac{5\left(2\sqrt{7}+\sqrt{5}\right)}{23}\)
- step3: Multiply the numbers:
\(\frac{10\sqrt{7}+5\sqrt{5}}{23}\)
The simplified form of \( \frac{5}{2 \sqrt{7}-\sqrt{5}} \) is \( \frac{10\sqrt{7}+5\sqrt{5}}{23} \).
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Simplifique esta solución The Deep Dive
To simplify the expression \( \frac{5}{2 \sqrt{7}-\sqrt{5}} \), we can multiply the numerator and the denominator by the conjugate of the denominator, which is \( 2 \sqrt{7} + \sqrt{5} \). This gives us: \[ \frac{5(2 \sqrt{7} + \sqrt{5})}{(2 \sqrt{7} - \sqrt{5})(2 \sqrt{7} + \sqrt{5})} \] The denominator simplifies using the difference of squares: \[ (2 \sqrt{7})^2 - (\sqrt{5})^2 = 4 \times 7 - 5 = 28 - 5 = 23 \] So now our expression looks like: \[ \frac{5(2 \sqrt{7} + \sqrt{5})}{23} \] Breaking it down, the final simplified form is: \[ \frac{10 \sqrt{7} + 5 \sqrt{5}}{23} \]
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