Question
Download Solution PDFFind the mean proportion between \(\left( {6 + \sqrt 8 } \right)\) and \(\left( {3 - \sqrt 2 } \right)\).
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept used:
Mean proportion of a and b = \(\sqrt {ab} \)
Calculation:
\(\sqrt{\left( {6 + \sqrt 8 } \right)\left( {3 - \sqrt 2 } \right)}\)
⇒ \(\sqrt{18-6\sqrt2+3\sqrt8-\sqrt{16}}\)
⇒ \(\sqrt{18-6\sqrt2+6\sqrt2-4}\)
⇒ \(\sqrt{18-4}\)
⇒ \(\sqrt {14} \)
∴ The required answer is \(\sqrt {14} \).
Last updated on Jul 17, 2025
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