Solution:

144 ÷ 2 = 72 (remainder is 0)
72 ÷ 2 = 36 (remainder is 0)
36 ÷ 2 = 18 (remainder is 0)
18 ÷ 2 = 9 (renainder is 0)
9 ÷ 3 = 3 (remainder is 0)

Now,
144 = 2 × 2 × 2 × 2 × 3 × 3
144 = 22 × 22 × 3
∴ $$\sqrt{144}$$ = 2 × 2 × 3
= 12

Solution:

576 ÷ 2 = 288 (remainder is 0)
288 ÷ 2 = 144 (remainder is 0)
144 ÷ 2 = 72 (remainder is 0)
72 ÷ 2 = 36 (remainder is 0)
36 ÷ 2 = 18 (remainder is 0)
18 ÷ 2 = 9 (remainder is 0)
9 ÷ 3 = 3 (remainder is 0)

Now,
576 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3
576 = 22 × 22 × 22 × 32
∴ $$\sqrt{576}$$ = 2 × 2 × 2 × 3
= 24

Solution:

= $$\sqrt{8}$$ × 3$$\sqrt{18}$$ × 2$$\sqrt{48}$$
= $$\sqrt{4 × 2}$$ × 3$$\sqrt{9 × 2}$$ × 2$$\sqrt{16 × 3}$$
= 2$$\sqrt{2}$$ × 3 × 3$$\sqrt{2}$$ × 2 × 4$$\sqrt{3}$$
= 144$$\sqrt{4}$$
= 144$$\sqrt{4 × 3}$$
= 144 × 2$$\sqrt{3}$$
= 288$$\sqrt{3}$$

Solution:

1.96 = $$\frac{196}{100}$$
∴ $$\sqrt{1.96}$$ = $$\sqrt{\frac{196}{100}}$$
= $$\frac{\sqrt{2 × 2 × 7 × 7}}{\sqrt{2 × 2 × 5 × 5}}$$
= $$\frac{\sqrt{2^2 × 7^2}}{\sqrt{2^2 × 5^2}}$$
= $$\frac{2 × 7}{2 × 5}$$
= $$\frac{14}{10}$$
= 1.4

Solution:

= $$\sqrt{\frac{256}{625}}$$
= $$\sqrt{\frac{2 × 2 × 2 × 2 × 2 × 2 × 2 × 2}{5 × 5 × 5 × 5}}$$
= $$\sqrt{\frac{2^2 × 2^2 × 2^2 × 2^2}{5^2 × 5^2}}$$
= $$\frac{2 × 2 × 2 × 2}{5 × 5}$$
= $$\frac{16}{25}$$