Math Problem Statement

Which of the following statements is true about the square root of 139?

  A. The square root of 139 has a value of 19,321.

  B. The square root of 139 has a value of 69.5.

  C. The square root of 139 has a value between 10 and 11.

  D. The square root of 139 has a value between 11 and 12.

Solution

To determine which statement is true, let’s approximate the square root of 139:

  1. Estimating Square Roots:

    • We know that 112=12111^2 = 121 and 122=14412^2 = 144.
    • Since 139 is between 121 and 144, the square root of 139 must lie between 11 and 12.
  2. Confirming the Correct Option:

    • This places 139\sqrt{139} between 11 and 12, making Option D the correct answer.

Correct Answer: D. The square root of 139 has a value between 11 and 12.

Would you like more details or have any questions about this?


Here are some related questions to deepen your understanding:

  1. How do we estimate square roots for numbers that aren’t perfect squares?
  2. What would the square root of a number slightly larger than 139 (like 140) be approximated as?
  3. How can you calculate a square root more precisely without a calculator?
  4. Why is 139\sqrt{139} closer to 12 than to 11?
  5. How can you tell if a number is a perfect square?

Tip: When estimating square roots, knowing the squares of numbers close to your target can help you quickly identify a range for the square root value.

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Math Problem Analysis

Mathematical Concepts

Square Roots
Estimation

Formulas

Estimating square roots by locating values between known squares

Theorems

Square Root Properties

Suitable Grade Level

Grades 6-8