Answered

I. Find the length of one side (s) of each square.

(I) Area = 25 m^2

(M) Area = 64 cm^2



II. Find the square root.

(T) $\sqrt{49}$

(O) $\sqrt{16}$

E$\sqrt{100}$

(N) $\sqrt{81}$

A$\sqrt{36}$

(O) $\sqrt{4}$

(I) $\sqrt{144}$

(G) $\sqrt{1}$

(H) $\sqrt{900}$

(L) $\sqrt{2,500}$

(F) $\sqrt{6,400}$

(K) $\sqrt{10,000}$



III. Simplify.

(O) $15^2$

(W) $11^2$

D$25^2$

(R) $\sqrt{225}$

(L) $\sqrt{121}$

(W) $\sqrt{625}$

(H) $\sqrt{16}+\sqrt{9}$

A$\sqrt{36}+\sqrt{64}$

(M) $\sqrt{25}-\sqrt{9}$

(S) $\sqrt{16+9}$

(M) $\sqrt{36+64}$

(O) $\sqrt{25-9}$

(Y) $\sqrt{0.25}$

(H) $\sqrt{0.81}$

(P) $\sqrt{0.01}$

Verified Answer :

  • Organize all arithmetic and square root expressions by calculating their numerical values.
  • Verify each calculation (e.g., \(\sqrt{144}=12\), \(\sqrt{0.01}=0.1\), \(25^2=625\)).
  • Map each calculated result to its provided exercise letter label.
  • Present the final mapping in a table for clarity and completeness.
  • The final answer is \(\boxed{\text{Table of mappings provided.}}\)

Explanation

  1. Organizing Exercises and Results

The provided exercises consist of three sections involving square roots and basic arithmetic related to squares. To solve the matching task, we organize each expression with its corresponding numerical answer and label.

Section I: Side Length of Squares

  • For \(s = 5 \text{ m}\), the side length is 5, labeled (1).
  • For \(s = 8 \text{ cm}\), the side length is 8, labeled (M).

Section II: Square Roots

  • \(\sqrt{49} = 7\) (T)
  • \(\sqrt{16} = 4\) (O)
  • \(\sqrt{100} = 10\) (E)
  • \(\sqrt{81} = 9\) (N)
  • \(\sqrt{36} = 6\) (A)
  • \(\sqrt{4} = 2\) (O)
  • \(\sqrt{144} = 12\) (1)
  • \(\sqrt{1} = 1\) (G)
  • \(\sqrt{900} = 30\) (H)
  • \(\sqrt{2,500} = 50\) (L)
  • \(\sqrt{6,400} = 80\) (F)
  • \(\sqrt{10,000} = 100\) (K)

Section III: Simplifications

  • \(15^2 = 225\) (O)
  • \(11^2 = 121\) (W)
  • \(25^2 = 625\) (D)
  • \(\sqrt{225} = 15\) (R)
  • \(\sqrt{121} = 11\) (L)
  • \(\sqrt{625} = 25\) (W)
  • \(\sqrt{16} + \sqrt{9} = 4 + 3 = 7\) (H)
  • \(\sqrt{36} + \sqrt{64} = 6 + 8 = 14\) (A)
  • \(\sqrt{25} - \sqrt{9} = 5 - 3 = 2\) (M)
  • \(\sqrt{16 + 9} = \sqrt{25} = 5\) (S)
  • \(\sqrt{36 + 64} = \sqrt{100} = 10\) (M)
  • \(\sqrt{25 - 9} = \sqrt{16} = 4\) (O)
  • \(\sqrt{0.25} = 0.5\) (Y)
  • \(\sqrt{0.81} = 0.9\) (H)
  • \(\sqrt{0.01} = 0.1\) (P)
  1. Matching Results to Labels

To effectively solve the matching task, we pair each numerical result with its corresponding label. This allows for a clear mapping between the provided exercises and their solutions.

| Result | Label | Result | Label |
| :--- | :--- | :--- | :--- |
| 5 | (1) | 0.1 | (P) |
| 8 | (M) | 0.5 | (Y) |
| 1 | (G) | 0.9 | (H) |
| 2 | (O), (M) | 7 | (T), (H) |
| 4 | (O), (O) | 9 | (N) |
| 5 | (S) | 10 | (E), (M) |
| 6 | (A) | 11 | (L) |
| 12 | (1) | 14 | (A) |
| 15 | (R) | 25 | (W) |
| 30 | (H) | 50 | (L) |
| 80 | (F) | 100 | (K) |
| 121 | (W) | 225 | (O) |
| 625 | (D) | | |

This table provides the definitive mapping of results to labels as requested by the task requirements.

Examples

Understanding how to correctly simplify square roots and calculate powers is essential for geometry and various engineering fields. For example, when calculating the diagonal of a square room using the Pythagorean theorem, \(d = \sqrt{s^2 + s^2} = s\sqrt{2}\), being proficient in these basic operations ensures accurate results. This practice of matching results helps reinforce mental math skills and fundamental algebraic proficiency.

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