The problem requires simplifying the given expressions involving square roots of products. The expressions are: (i) $\sqrt{25 \times 16}$ (ii) $\sqrt{36 \times 4}$ (iii) $\sqrt{49 \times 81}$ (iv) $\sqrt{100 \times 121}$ (v) $\sqrt{144 \times 169}$

1. Problem Description

The problem requires simplifying the given expressions involving square roots of products. The expressions are:

(i) $\sqrt{25 \times 16}$

(ii) $\sqrt{36 \times 4}$

(iii) $\sqrt{49 \times 81}$

(iv) $\sqrt{100 \times 121}$

(v) $\sqrt{144 \times 169}$

2. Solution Steps

We will use the property $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$.

(i) $\sqrt{25 \times 16} = \sqrt{25} \times \sqrt{16} = 5 \times 4 = 20$

(ii) $\sqrt{36 \times 4} = \sqrt{36} \times \sqrt{4} = 6 \times 2 = 12$

(iii) $\sqrt{49 \times 81} = \sqrt{49} \times \sqrt{81} = 7 \times 9 = 63$

(iv) $\sqrt{100 \times 121} = \sqrt{100} \times \sqrt{121} = 10 \times 11 = 110$

(v) $\sqrt{144 \times 169} = \sqrt{144} \times \sqrt{169} = 12 \times 13 = 156$

3. Final Answer

(i) 20

(ii) 12

(iii) 63

(iv) 110

(v) 156