Math Problem Statement

Evaluate each of the following on the calculator and round the answers to the indicated place.

Solution

The image contains a math worksheet that asks for square root calculations rounded to specific decimal places. Let's go through and solve each problem:

  1. 7\sqrt{7} (Rounded to the tenths place): 72.645751311\sqrt{7} \approx 2.645751311 ⇒ Rounded to the tenths: 2.6

  2. 20\sqrt{20} (Rounded to the hundredths place): 204.472135955\sqrt{20} \approx 4.472135955 ⇒ Rounded to the hundredths: 4.47

  3. 252\sqrt{5} (Rounded to the thousandths place): 25=2×2.2360679774.4721359552\sqrt{5} = 2 \times 2.236067977 \approx 4.472135955 ⇒ Rounded to the thousandths: 4.472

  4. 8-\sqrt{8} (Rounded to the nearest whole number): 8=2.828427124-\sqrt{8} = -2.828427124 ⇒ Nearest whole number: -3

  5. 3\sqrt{3} (Rounded to the tenths place): 31.732050808\sqrt{3} \approx 1.732050808 ⇒ Rounded to the tenths: 1.7

  6. 150\sqrt{150} (Rounded to the thousandths place): 15012.24744871\sqrt{150} \approx 12.24744871 ⇒ Rounded to the thousandths: 12.247


Let me know if you'd like further clarification on any steps!

Follow-up questions:

  1. What are the steps for calculating square roots by hand?
  2. Can all square roots be simplified exactly?
  3. How is the rounding process affected by different decimal places?
  4. Why is 150\sqrt{150} not a perfect square?
  5. What is the difference between irrational and rational numbers?

Tip: Always double-check your rounding, especially when asked to round to different decimal places.

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Math Problem Analysis

Mathematical Concepts

Square Roots
Rounding
Decimal Places

Formulas

√x
2√x

Theorems

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Suitable Grade Level

Grades 7-9