The square root of $0.0009$ is:

Question

Examoogle · Accepted Answer

The correct answer is Option D: $0.03$. Count the number of decimal places. Here, 0.0009 has 4 decimal places. The square root will have half that many decimal places (4 / 2 = 2). Since the square root of 9 is 3, the result must be 0.03.

Step-by-Step Solution & Concepts:
Shortcut Trick: Count the number of decimal places. Here, 0.0009 has 4 decimal places. The square root will have half that many decimal places (4 / 2 = 2). Since the square root of 9 is 3, the result must be 0.03.

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

Given: We need to find the square root of 0.0009.

Steps: Convert decimal to fraction: Express the decimal $0.0009$ as a fraction to simplify calculation: $0.0009 = \frac{9}{10000}$.. Apply square root property: Calculate the square root of the fraction: $\sqrt{\frac{9}{10000}} = \frac{\sqrt{9}}{\sqrt{10000}}$.. Convert back to decimal: Convert the fraction $\frac{3}{100}$ back into a decimal format: $0.03$.

Answer: A is correct because the square root of $0.0009$ is $\sqrt{0.0009} = \sqrt{9 	imes 10^{-4}} = 3 	imes 10^{-2} = 0.03$.

Exam Tip: This logic is essential for solving questions in physics (e.g., calculations involving resistance or charge density) and quantitative aptitude sections where rapid decimal manipulation is required.

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Discussion (0)

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)