Calculate the Square Root of 52: Finding the Closest Approximation

Rounding to Nearest Ten

52 ? 52\approx\text{ ?}

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Step-by-step written solution

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1

Understand the problem

52 ? 52\approx\text{ ?}

2

Step-by-step solution

To solve this problem, we will round the number 52 to the nearest 10. Here's the step-by-step explanation:

  • Step 1: Identify the ones digit of 52, which is 2.
  • Step 2: Apply the rounding rule: if the ones digit is less than 5, round down; if it is 5 or more, round up.
  • Step 3: Since the ones digit of 52 is 2, which is less than 5, we will round down to the nearest multiple of 10.
  • Step 4: The nearest multiple of 10 below 52 is 50.

Therefore, when 52 is rounded to the nearest 10, it becomes 50 50 .

3

Final Answer

50 50

Key Points to Remember

Essential concepts to master this topic
  • Rule: Look at the ones digit to determine rounding direction
  • Technique: Since 2 < 5, round down: 52 → 50
  • Check: Verify 50 is closer to 52 than 60 (difference is 2) ✓

Common Mistakes

Avoid these frequent errors
  • Rounding to the wrong place value
    Don't round 52 to the nearest hundred (100) when asked for nearest ten! This gives an answer that's 48 units away instead of 2 units. Always identify the place value you're rounding to first.

Practice Quiz

Test your knowledge with interactive questions

\( 52\approx\text{ ?} \)

FAQ

Everything you need to know about this question

Why do we look at the ones digit when rounding to tens?

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The ones digit tells us whether we're closer to the ten below or the ten above. If it's 0-4, we're closer to the lower ten. If it's 5-9, we're closer to the higher ten.

What happens if the ones digit is exactly 5?

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When the ones digit is exactly 5, we round up to the next ten. For example, 45 rounds up to 50, and 135 rounds up to 140.

How do I know which multiples of 10 to compare?

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Look at the tens digit! For 52, the tens digit is 5, so compare with 50 (5 tens) and 60 (6 tens). Pick whichever is closer.

Is there a quick way to check my rounding?

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Yes! Calculate the distance from your original number to your rounded answer. For 52 → 50, the distance is |52 - 50| = 2. This should be 5 or less for correct rounding to tens.

Can I round negative numbers the same way?

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Absolutely! The same rules apply. For example, -52 would round to -50 because the ones digit is still 2, which is less than 5.

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