If $ (584)^2 = 3,41,056 $, then the value of square root of $ 34.1056 $ is:

Question

Examoogle · Accepted Answer

The correct answer is Option D: 84. Count the number of decimal places in the radicand ($n$ digits). The square root will always have exactly $n/2$ decimal places. Here, $34.1056$ has 4 decimal places, so the result must have 2 decimal places.

Step-by-Step Solution & Concepts:
Shortcut Trick: Count the number of decimal places in the radicand ($n$ digits). The square root will always have exactly $n/2$ decimal places. Here, $34.1056$ has 4 decimal places, so the result must have 2 decimal places.

Formula Used: $$\sqrt{\frac{x}{10^{2n}}} = \frac{\sqrt{x}}{10^n}$$

Given: We are given that $584^2 = 3,41,056$. We need to find the value of $\sqrt{34.1056}$.

Steps: Analyze the given relation: We know that $(584)^2 = 3,41,056$. Therefore, $\sqrt{3,41,056} = 584$.. Rewrite the target number: Express $34.1056$ as a fraction to identify the power of 10 in the denominator.. Calculate the square root: Apply the square root to the fraction using the property $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$.

Answer: D is correct because the square root of $34.1056$ results in $5.84$ after correctly shifting the decimal point by two places.

Exam Tip: This decimal shift logic is identical to scientific notation normalization used in Physics for magnitude calculations.

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