Math Problem Statement

Solution

Let's complete the tables by following the examples given.

TABLE 1A

  1. 425\sqrt{4 \cdot 25} simplifies to 100\sqrt{100} which is equal to 1010.
  2. 936\sqrt{9 \cdot 36} simplifies to 324\sqrt{324} which is equal to 1818.
  3. 164\sqrt{16 \cdot 4} simplifies to 64\sqrt{64} which is equal to 88.
  4. 36+100\sqrt{36 + 100} simplifies to 136\sqrt{136} which is approximately 11.6611.66 (since 136 is not a perfect square).

TABLE 1B

  1. 425\sqrt{4} \cdot \sqrt{25} simplifies to 252 \cdot 5 which is equal to 1010.
  2. 936\sqrt{9} \cdot \sqrt{36} simplifies to 363 \cdot 6 which is equal to 1818.
  3. 164\sqrt{16} \cdot \sqrt{4} simplifies to 424 \cdot 2 which is equal to 88.
  4. 36100\sqrt{36} \cdot \sqrt{100} simplifies to 6106 \cdot 10 which is equal to 6060.

Do you want further details on any of these calculations or have any questions?

Here are 5 questions you might want to ask:

  1. How do you simplify square root expressions involving products?
  2. How do you handle square roots of non-perfect squares?
  3. Can you explain the process of simplifying square roots step-by-step?
  4. What are some common perfect squares to memorize?
  5. How do you approximate square roots of non-perfect squares?

Tip: When simplifying expressions with square roots, always look for perfect squares to make calculations easier.

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Math Problem Analysis

Mathematical Concepts

Square Roots
Simplification of Square Roots

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9