Square and square roots 3

Math Problems

1. Given that $ \sqrt{1521} = 39 $, find the value of $ \sqrt{0.1521} + \sqrt{15.21} $.

   Solution:

   We know that $ \sqrt{1521} = 39 $, so if we divide 1521 by 10000 and 100 respectively we can find the square root of $ 0.1521 $ and $ 15.21 $.

   Therefore, $ \sqrt{0.1521} = 0.39 $ and $ \sqrt{15.21} = 3.9 $.

   Adding these together, $ \sqrt{0.1521} + \sqrt{15.21} = 0.39 + 3.9 = 4.29 $.

2. Find the sum of the series $ 1 + 3 + 5 + 7 + \cdots $ up to n terms.

   Solution:

   This is the sum of the first $ n $ odd numbers, and it is well known that the sum of the first $ n $ odd numbers is $ n^2 $.

   Therefore, $ 1 + 3 + 5 + 7 + \cdots $ up to $ n $ terms is equal to $ n^2 $.