Consider this puzzle: What is the square root of -1? Class 9

Consider this puzzle: What is the square root of -1? Class 9

Question 1.

Consider this puzzle: What is the square root of -1? Class 9

Answer:

We know that 1 × 1 = 1.

We also know that (-1) × (-1) = 1.

There is no real number that, when multiplied by itself, results in a negative number.

Thus, $\sqrt{-1}$ cannot exist on number line.

Question 2.

Convert the following rational numbers in the form of a terminating decimal or non-terminating and repeating decimal, whichever the case may be, by the process of long division: Class 9

i. $\frac{3}{50}$

ii. $\frac{2}{9}$

Solution:

i. $\frac{3}{50}$

50 = 2 × 5²

Since denominator has prime factors other than 2 and 5.

∴ $\frac{3}{50}$ is a terminating decimal.

Verification:

∴ $\frac{3}{50}$ which is a terminating decimal.

ii. $\frac{2}{9}$

9 = 3²

Since denominator has prime factors other than 2 and 5.

∴ $\frac{2}{9}$ is a non-terminating repeating decimal.

Verification:

∴ $\frac{2}{9}$ = 0.2222...., which is a non-terminating repeating decimal