Calculate the Square Root: Finding the Approximate Value of √465

To solve this problem, we'll follow these steps:

• Step 1: Identify the tens and units digits in 465.
• Step 2: Apply the rounding rule for the nearest ten.
• Step 3: Determine the rounded value based on the rule.

Now, let's work through each step:
Step 1: The number 465 has 6 in the tens place and 5 in the units place.

Step 2: To round to the nearest ten, we look at the units digit (5). According to rounding rules, if the digit is 5 or more, we round up.

Step 3: Since the units digit of 465 is 5, we round 460 up to 470.

Therefore, the rounded value of 465 to the nearest ten is $470$.