The square root of $ 6084 $ is:

Question

Examoogle · Accepted Answer

The correct answer is Option C: 78. Check the last digit (4); the root must end in 2 or 8 ($2^2=4, 8^2=64$). Estimate: $70^2 = 4900$ and $80^2 = 6400$. Since 6084 is between 4900 and 6400 but closer to 6400, the answer is 78.

Step-by-Step Solution & Concepts:
Shortcut Trick: Check the last digit (4); the root must end in 2 or 8 ($2^2=4, 8^2=64$). Estimate: $70^2 = 4900$ and $80^2 = 6400$. Since 6084 is between 4900 and 6400 but closer to 6400, the answer is 78.

Formula Used: $$\sqrt{6084} = x$$

Given: Number to find the square root of is 6084.

Steps: Analyze the number: We need to find the value of $\sqrt{6084}$. The number ends in 4, so the last digit of the square root must be either 2 or 8.. Estimate the range: Find the squares of multiples of 10 near 6084. We know $70^2 = 4900$ and $80^2 = 6400$. The root must be between 70 and 80.. Narrow down the choice: Check the square of 75 to compare. $75^2 = (7 	imes 8) 	imes 100 + 25 = 5625$. Since $6084 > 5625$, the root must be greater than 75. Therefore, it must be 78.

Answer: C is correct because the square root of 6084 is exactly 78.

Exam Tip: This method is useful for all competitive exams to quickly verify squares of numbers ending in 1, 4, 5, 6, and 9 without long division.

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