Question
Download Solution PDFIf 5\(\sqrt{3}\) + \(\sqrt{75}\) = 17.32, then the value of 14\(\sqrt{3}\) + \(\sqrt{108}\) is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
5\(\sqrt{3}\) + \(\sqrt{75}\) = 17.32
Calculation:
5\(\sqrt{3}\) + \(\sqrt{75}\) = 17.32
⇒ 5\(\sqrt{3}\) + \(5\sqrt{3}\) = 17.32
⇒ \(10\sqrt{3}\) = 17.32
⇒ \(\sqrt{3}\) = 17.32/10
⇒ \(\sqrt{3}\) = 1.732 ....(1)
Now,
14\(\sqrt{3}\) + \(\sqrt{108}\)
⇒ 14\(\sqrt{3}\) + \(\sqrt{36 × 3}\)
⇒ 14\(\sqrt{3}\) + \(6\sqrt{3}\)
⇒ \(20\sqrt{3}\)
⇒ 20 × 1.732 (From 1)
⇒ 34.64
∴ The value of 14\(\sqrt{3}\) + \(\sqrt{108}\) is 34.64.
Last updated on Jun 13, 2025
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