Math Problem Statement

The original question submitted by the user involves determining values of square roots and their approximate positions between whole numbers or on a number line, as well as a comparison between values of different square roots.

Solution

Let's solve the problems one by one:

  1. The value of 19\sqrt{19} falls between which two whole numbers?
  • 16=4\sqrt{16} = 4 and 25=5\sqrt{25} = 5.
  • So, 19\sqrt{19} is between 4 and 5.
  • Answer: D. 4 and 5
  1. The value of 30\sqrt{30} falls between which two whole numbers?
  • 25=5\sqrt{25} = 5 and 36=6\sqrt{36} = 6.
  • So, 30\sqrt{30} is between 5 and 6.
  • Answer: A. 5 and 6
  1. Using the number line, determine which point most accurately portrays the value of 8\sqrt{8}.
  • 4=2\sqrt{4} = 2 and 9=3\sqrt{9} = 3.
  • 8\sqrt{8} is slightly less than 3, around 2.8, which appears closest to Point N.
  1. Which statement is true about the values of 10\sqrt{10} and 15\sqrt{15}?
  • 103.16\sqrt{10} \approx 3.16 and 153.87\sqrt{15} \approx 3.87.
  • Both 10\sqrt{10} and 15\sqrt{15} fall between 3 and 4.
  • Answer: A. The value of 10\sqrt{10} and the value of 15\sqrt{15} both fall between 3 and 4.

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Math Problem Analysis

Mathematical Concepts

Square roots
Number sense
Estimation using square roots

Formulas

\(\sqrt{n}\) for approximating square roots of non-perfect squares

Theorems

The square of a number theorem
Inequalities for square roots between consecutive integers

Suitable Grade Level

Grades 6-8