Question
Download Solution PDFGiven that \(\sqrt{4096} \) = 64.
What will be the value of \(\sqrt{4096} + \sqrt{40.96} + \sqrt{0.004096} \) ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
\(\sqrt{4096} \) = 64
Concept Used:
\(\sqrt{\frac{a}{100}} = \frac{\sqrt{a}}{10}\)
\(\sqrt{\frac{a}{10000}} = \frac{\sqrt{a}}{100}\)
Calculation:
\(\sqrt{4096} \) = 64
\(\sqrt{40.96} = \sqrt{\frac{4096}{100}} = \frac{\sqrt{4096}}{\sqrt{100}} = \frac{64}{10} = 6.4\)
\(\sqrt{0.004096} = \sqrt{\frac{4096}{1000000}} = \frac{\sqrt{4096}}{\sqrt{1000000}} = \frac{64}{1000} = 0.064\)
\(\sqrt{4096} + \sqrt{40.96} + \sqrt{0.004096} \) = 64 + 6.4 + 0.064
⇒ 64.000 + 6.400 + 0.064
⇒ 70.464
∴ The value of \(\sqrt{4096} + \sqrt{40.96} + \sqrt{0.004096} \) is 70.464.
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