Square and square roots part -3

Math Problems and Solutions

1. Question: Amit walks 16 m south from his friend's house while returning, he walks diagonally from his friend's house to reach back to his house. What distance did he walk while returning?

   Solution: Amit walked 16 m south from his friend's house. Let's assume his house is east of his friend's house. The distance he walked while returning is the diagonal of a square with sides of 16 m (because the distance he initially walked south is the same as the distance east). Using the Pythagorean theorem, the diagonal is \(\sqrt{16^2 + 16^2} = \sqrt{2} \times 16 \approx 22.63\) m.

2. Question: Find the square root of the following.

   (a) \(16 \frac{169}{441}\)

   (b) \(5.774409\)

   (c) \(\frac{841}{1521}\)

   Solution:

   (a) \(16 \frac{169}{441} = 16 + \frac{169}{441} = 16 + \frac{13}{21} = \frac{357}{21}\). The square root of \(\frac{357}{21}\) is \(\sqrt{\frac{357}{21}} = \frac{\sqrt{357}}{\sqrt{21}} \approx 4.49\).

   (b) The square root of \(5.774409\) is \(\sqrt{5.774409} \approx 2.4026\).

   (c) \(\frac{841}{1521}\) can be simplified as \(\frac{29}{39}\). The square root of \(\frac{29}{39}\) is \(\sqrt{\frac{29}{39}} = \frac{\sqrt{29}}{\sqrt{39}} \approx 0.76\).