Which condition confirms it is a perfect square?
  • Even number
  • Odd number
  • Factors can be paired
  • Ends with 4
What is the sum of first 6 odd numbers?
  • 30
  • 36
  • 40
  • 42
Given = 23104, what is the value of ? (Hint )
  • 23104 + 153
  • 23104 + 306 + 1
  • 23104 + 305
  • 23104 + 307
  • 23104 + 150
A natural number is not a perfect square if it cannot be expressed as a sum of successive odd natural numbers starting from 1.
  • True
  • False
The square roots of 64 are +8 and -8.
  • True
  • False
Akhil cannot cut a handkerchief of side 15 cm from the given cloth because:
  • the side of the original square cloth is less than 15 cm.
  • the cloth is not square in shape.
  • the cloth is too thick to cut.
  • the cloth is already cut into pieces.
Find the side length of the original square cloth.
  • Side length = √125 ≈ 11.18 cm
  • Side length = √100 ≈ 10 cm
  • Side length = √144 ≈ 12 cm
  • Side length = √81 ≈ 9 cm
What is the largest possible square handkerchief (with integer side length) that Akhil can cut from the cloth?
  • 11 cm.
  • 8 cm.
  • 9 cm.
  • 10 cm.
How much cloth area will remain unused after cutting the largest possible square handkerchief?
  • Unused area = 125 - 121 = 4 cm^2
  • Unused area = 125 - 100 = 25 cm^2
  • Unused area = 125 - 81 = 44 cm^2
  • Unused area = 125 - 64 = 61 cm^2
Perfect squares help in solving real-life problems by:
  • determining the maximum possible size of square objects that can be cut from a given area, optimizing material usage.
  • finding the total number of objects in a group.
  • measuring the perimeter of circular objects.
  • calculating the volume of irregular shapes.
If a number contains 4 zeros at the end, how many zeros will its square have at the end?
  • 8 zeros
  • 4 zeros
  • 2 zeros
  • 6 zeros
The parity (even or odd) of a number and its square is:
  • always the same
  • always different
  • sometimes the same, sometimes different
  • cannot be determined
A school wants to create a square playground using tiles. They have 2000 tiles. Can they make a perfect square?
  • No, because 2000 is not a perfect square.
  • Yes, because 2000 is a perfect square.
  • Yes, because 2000 is an even number.
  • No, because 2000 is too small.
Case Study 1: The Architect's Design An architect is designing a square courtyard with an area of 576 square meters. (a) Calculate the length of one side of the courtyard using the prime factorization method.
  • 24 meters
  • 12 meters
  • 36 meters
  • 18 meters
If the architect decides to double the side length, by how many times will the area of the courtyard increase?
  • The area will increase by 4 times.
  • The area will increase by 2 times.
  • The area will increase by 8 times.
  • The area will increase by 16 times.
A gardener has 1,000 plants and wants to arrange them in a square grid such that the number of rows equals the number of columns. Find the maximum number of plants they can use for this square and how many plants will be left over.
  • Maximum number of plants used: 961 (31 x 31). Plants left over: 39.
  • Maximum number of plants used: 900 (30 x 30). Plants left over: 100.
  • Maximum number of plants used: 1024 (32 x 32). Plants left over: 0.
  • Maximum number of plants used: 980 (28 x 35). Plants left over: 20.
The mathematical origin of the Sanskrit term Varga-mula relates to the English word "root" as both refer to which value?
  • The value that, when multiplied by itself, gives the original number
  • The value that, when added to itself, gives the original number
  • The value that, when subtracted from itself, gives zero
  • The value that, when divided by itself, gives one
Explain why adding the 4th triangular number to the 3rd triangular number results in a perfect square.
  • 6 + 10 = 16, which is a perfect square (4 x 4).
  • 3 + 6 = 9, which is a perfect square (3 x 3).
  • 1 + 3 = 4, which is a perfect square (2 x 2).
  • 10 + 15 = 25, which is a perfect square (5 x 5).
A school wants to tile a square courtyard. The total area is 484 m². What will be the length of one side of the courtyard?
  • 22 meters
  • 18 meters
  • 24 meters
  • 20 meters
A school wants to tile a square courtyard. The total area is 484 m². If each tile is 1 m x 1 m, how many tiles are needed?
  • 484 tiles
  • 22 tiles
  • 242 tiles
  • 968 tiles
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