Cube and cube roots part-2

Solutions

1. Question 9: Calculate $\sqrt{208+\sqrt{2304}}$

   Solution: First, calculate the square root of 2304 and then add it to 208 before taking the square root of the sum.

   $$ = \sqrt{208+\sqrt{2304}} $$ $$ = \sqrt{208+48} $$ $$ = \sqrt{256} $$ $$ = 16 $$

2. Question 10: Calculate $\sqrt{0.0016}$

   Solution: The square root of 0.0016 is:

   $$ = \sqrt{0.0016} $$ $$ = \sqrt{16 \times 10^{-4}} $$ $$ = \sqrt{16} \times \sqrt{10^{-4}} $$ $$ = 4 \times 10^{-2} $$ $$ = 0.04 $$

3. Question 11: Given that $\sqrt{1521} = 39$, find the value of $\sqrt{0.1521}+\sqrt{15.21}$.

   Solution: This seems to be an error, because $\sqrt{1521}$ should be equal to 39. Assuming the correct value is $\sqrt{1521} = 39$, let's calculate:

   $$ = \sqrt{0.1521} + \sqrt{15.21} $$ $$ = \sqrt{\frac{1521}{10000}} + \sqrt{\frac{1521}{100}} $$ $$ = \frac{39}{100} + \frac{39}{10} $$ $$ = 0.39 + 3.9 $$ $$ = 4.29 $$

4. Question 12: 1 + 3 + 5 + 7 + ... up to n terms is equal to?

   Solution: This is the sum of the first n odd numbers. The sum of the first n odd numbers is equal to $n^2$. Therefore,

   $$ 1 + 3 + 5 + 7 + ... = n^2 $$