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Find the smallest square number that is divisible by each of the following numbers: 4, 9 and 10.
To find the smallest square divisible by 4, 9 and 10, we first compute their LCM: 4 = 2², 9 = 3², 10 = 2 × 5 ⇒ LCM = 2² × 3² × 5 = 180. Now find the smallest perfect square that includes all these prime factors in even powers. 900 = 2² × 3² × 5² = 30², which is a perfect square and divisible by 180.Read more
To find the smallest square divisible by 4, 9 and 10, we first compute their LCM:
4 = 2², 9 = 3², 10 = 2 × 5 ⇒ LCM = 2² × 3² × 5 = 180.
Now find the smallest perfect square that includes all these prime factors in even powers. 900 = 2² × 3² × 5² = 30², which is a perfect square and divisible by 180.
Answer: 900.
For more NCERT Solutions for Class 8 Mathematics Ganita Prakash Chapter 1 A Square and A Cube Extra Questions & Answer:
https://www.tiwariacademy.com/ncert-solutions/class-8/maths/ganita-prakash-chapter-1/
See lessFind the length of the side of a square whose area is 441 m².
If the area of a square is 441 m², then the side is the square root of 441. Since 21 × 21 = 441, √441 = 21. So, the side of the square is 21 meters long. This follows the formula: Area = side × side → side = √Area This method helps in reverse-calculating side lengths from square areas. For moRead more
If the area of a square is 441 m², then the side is the square root of 441. Since 21 × 21 = 441, √441 = 21. So, the side of the square is 21 meters long. This follows the formula:
Area = side × side → side = √Area
This method helps in reverse-calculating side lengths from square areas.
For more NCERT Solutions for Class 8 Mathematics Ganita Prakash Chapter 1 A Square and A Cube Extra Questions & Answer:
https://www.tiwariacademy.com/ncert-solutions/class-8/maths/ganita-prakash-chapter-1/
See lessGiven 125² = 15625, what is the value of 126²? (i) 15625 + 126 (ii) 15625 + 26² (iii) 15625 + 251 (iv) 15625 + 253 (v) 15625 + 51²
To find 126² using 125², apply the identity: (a+1)² = a² + 2a + 1 Here, a = 125, so 126² = 125² + 2×125 + 1 = 15625 + 250 + 1 = 15625 + 251 Therefore, the correct option is (iv) 15625 + 251. This method allows quick calculations using known square values and avoids complete re-multiplication. Read more
To find 126² using 125², apply the identity:
(a+1)² = a² + 2a + 1
Here, a = 125, so
126² = 125² + 2×125 + 1 = 15625 + 250 + 1 = 15625 + 251
Therefore, the correct option is (iv) 15625 + 251. This method allows quick calculations using known square values and avoids complete re-multiplication.
For more NCERT Solutions for Class 8 Mathematics Ganita Prakash Chapter 1 A Square and A Cube Extra Questions & Answer:
https://www.tiwariacademy.com/ncert-solutions/class-8/maths/ganita-prakash-chapter-1/
See lessWhich one among 64², 108², 292², 36² has last digit 4?
Let’s compute the squares: 64² = 4096 (last digit is 6) 108² = 11664 (last digit is 4) 292² = 85264 (last digit is 4) 36² = 1296 (last digit is 6) Among these, only 108² and 292² end in 4. So, the correct options with a unit digit 4 are 108² and 292². The question asks for which square ends in 4 andRead more
Let’s compute the squares:
64² = 4096 (last digit is 6)
108² = 11664 (last digit is 4)
292² = 85264 (last digit is 4)
36² = 1296 (last digit is 6)
Among these, only 108² and 292² end in 4. So, the correct options with a unit digit 4 are 108² and 292². The question asks for which square ends in 4 and both satisfy it.
For more NCERT Solutions for Class 8 Mathematics Ganita Prakash Chapter 1 A Square and A Cube Extra Questions & Answer:
https://www.tiwariacademy.com/ncert-solutions/class-8/maths/ganita-prakash-chapter-1/
See lessWhich of the following numbers are not perfect squares? (i) 2032 (ii) 2048 (iii) 1027 (iv) 1089
Among the given numbers, only 1089 is a perfect square (33² = 1089). The other numbers—2032, 2048 and 1027—are not perfect squares because they don’t have whole number square roots. If you try to factor or estimate their roots, you'll find they lie between squares, proving they’re not perfect squareRead more
Among the given numbers, only 1089 is a perfect square (33² = 1089). The other numbers—2032, 2048 and 1027—are not perfect squares because they don’t have whole number square roots. If you try to factor or estimate their roots, you’ll find they lie between squares, proving they’re not perfect squares. So, the correct answer is: Only 1089 is a perfect square; the rest are not.
For more NCERT Solutions for Class 8 Mathematics Ganita Prakash Chapter 1 A Square and A Cube Extra Questions & Answer:
https://www.tiwariacademy.com/ncert-solutions/class-8/maths/ganita-prakash-chapter-1/
See less