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:

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