Answer:
The answer is given below
Step-by-step explanation:
1) Find the possible ones place digit in the square root of the following
a) 2039184
The number 2039184 ends with 4, therefore the square root of the number can either end in 2 or 8
2² = 4, √4 = 2
8² = 64, √64 = 8
b) 10,004,569
The number 10,004,569 ends with 9, therefore the square root is the number will end in 3
3² = 9, √9 = 3
2) How many natural numbers lie between the squares of 41 and 42
42² = 1764 and 41² = 1681
Therefore the numbers that lie between 1764 and 1681 = (1764 - 1681) - 1 = 83 - 1 = 82
3) What will be the value of ‘ x’ in Pythagorean triplet (41, 9, x)
Pythagorean consist of three positive numbers a, b, c such that a² + b² = c². Therefore: x² + 9² = 41²
x² = 41² - 9² = 1681 - 81
x² = 1600
x = √1600 = 40
4) Check whether 15028 is a perfect square
15028 = 2 × 2 × 13 × 17 × 17
15028 = 2² × 13 × 17²
It is not a perfect square. If it is divided by 13 it becomes a perfect square, that is:
15028/13 = 2² × 17²
15028/13 = (2 × 17)² = 34²
34² = 15028/13
34² = 1156
The square root of the new number formed is 34 (i.e √1156)
5) A gardener has 5190 plants. He wants to plant in such a way that the number of rows and columns remains the same.
let the number if rows be x. Since the rows and columns are the same, the number of columns = x.
x² = 5190
x = √5190 = 72² + 6.
Therefore at least six plant would be left out
so that 
, which can be written as perfect squares.
are perfect square trinomials.
