Answered

I. Find the length of a side of a square with:

Area = 400 sq ft



II. Find the square root.

(N) $\sqrt{81}$

(T) $\sqrt{49}$

(O) $\sqrt{16}$

E$\sqrt{100}$

(G) $\sqrt{1}$

(R) $\sqrt{36}$

(O) $\sqrt{4}$

(I) $\sqrt{144}$

(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 :

  • Part I: The side length of a square with area \(400\) sq ft is \(s = \sqrt{400} = \boxed{20 \text{ ft}}\).
  • Part II: The evaluated square roots are:

(N) 9, (T) 7, (O) 4, (E) 10, (G) 1, (R) 6, (O) 2, (I) 12, (H) 30, (L) 50, (F) 80, (K) 100.

Explanation

  1. Part I: Finding the Side Length of a Square

For Part I, we are asked to find the side length \(s\) of a square with a given area. The formula for the area of a square with side length \(s\) is \(Area = s^2\). Given that the area is \(400\) sq ft, we have the equation \(s^2 = 400\). Taking the square root of both sides, we find \(s = \sqrt{400} = 20\). Thus, the length \(s\) is \(20\) ft.

  1. Part II: Evaluating Square Roots

For Part II, we evaluate the square root of each number provided in the list:

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

All these values are calculated by identifying the number that, when multiplied by itself, results in the radicand. For example, \(\sqrt{900} = 30\) because \(30 \times 30 = 900\).

Examples

Understanding square roots is essential in geometry and construction. For example, if you are planning to build a square garden with an area of \(100\) square meters, you need to know the length of the fencing for each side. By calculating the square root of the area, \(\sqrt{100} = 10\), you determine that you need \(10\) meters of fencing per side to enclose your garden area. This basic application of roots ensures accurate measurements for any square-based project.

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