Real numbers in everyday life (Class- 8, Experience-2)

[Exercise- Page 45]

E.2.1. Long jump is a fun game in sports competitions. Suppose you are to jump and touch a wall 10 m away. However, you can only jump halfway to the goal in every jump. For example, in the first jump, you cross 10 2 = 5m In the next jump, you cross 52 = 2.5m and so on. Can you find many how many jumps you need to get to the wall in this way?

Solution:

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E.2.2. In a square-shaped mango garden there are 1369 mango trees. If there is an equal number of mango trees along the length and breadth of the garden, then what’s the number of mangoes in each row? Give logical reasons for your answer. If the distance between any two trees is 100 ft, then what’s the approximate area of the garden?

Solution:

Number of mangoes in each row:

The total number of mango trees is given as 1369. To find the number of trees in each row, we take the square root of 1369.

Number of mangoes in each row= $\sqrt{1369}$ = 37

So, there are 37 mango trees in each row.

 

Approximate area of the garden:

Since the garden is square-shaped, and there are 37 mango trees in each row, we can calculate the length of one side of the square garden by multiplying the number of trees in each row by the distance between any two trees.

Length of one side of the garden= 37×100 ft = 3700 ft

Since the garden is square-shaped, the length and breadth are the same. Therefore, the area of the garden is the square of the length of one side.

Area of the garden= (Length of one side${)}^2$ = ${3700}^2$ sq. ft = 13690000 sq. ft

So, the approximate area of the garden is 13,690,000 square feet.

E.2.3. Find the square root of all the perfect squares from 1 to 100. Also, find the cube root of all the perfect cubes from 1 to 100.

Solution:

 let's find the square roots of perfect squares from 1 to100:

√1 = 1

√4 = 2

√9 = 3

√16 = 4

√25 = 5

√36 = 6

√49 = 7

√64 = 8

√81 = 9

√100 = 10

Now, let's find the cube roots of perfect cubes from 1 to 100:

∛1 = 1

∛8 = 2

∛27 = 3

∛64 = 4

Note that there are no perfect cubes between 1 and 100 other than 1, 8, 27, and 64

E.2.4. On a number line the points P, Q, R, S, T, U, A and B are located such that TR = RS = SU and AP = PQ = QB. Find the values of the rational numbers P, Q, R and S.

Solution:

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E.2.5. Are the numbers below rational or irrational? Explain. 

8.929292.…, 

0.1010010001…,  

6534.789749…..,  

2.18281828,  

0.122333..…

Solution:

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E.2.6. Perform addition, subtraction, multiplication and division with the numbers 2√ 2 + 5√ 8  and 7√ 8 - 4√ 2 . Hence, represent the answers on a number line.

Solution:

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E.2.7. Simplify: ∛ 3   5 + ∛ 9   5 - ∛ 81 

Solution:

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E.2.8. Nisith Chakma has two square-shaped vegetable gardens. The length of one garden is 2√ 2  units, and the area of the other is twice the area of the first. What’s the length of the other garden?

Solution:

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E.2.9. You have two cube-shaped boxes. One box has a volume of 16 m³ and the other has a volume of 11 m³. What are the lengths of the sides of each box? If the boxes are split and made into a single cubic box of volume equal to the sum of the volumes of the two boxes, then what’s the length of the sides of the new box?

Solution:

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