Secondary School (English Medium) (5 to 8) Class 8 - CBSE Question Bank Solutions

Find the square root the following by prime factorization. 

3013696

Find the smallest number by which 180 must be multiplied so that it becomes a perfect square. Also, find the square root of the perfect square so obtained.

Find the smallest number by which 147 must be multiplied so that it becomes a perfect square. Also, find the square root of the number so obtained.

Express each of the following product as a monomials and verify the result in each case for x = 1:
(3x) × (4x) × (−5x)

Find the smallest number by which 3645 must be divided so that it becomes a perfect square. Also, find the square root of the resulting number. 

Find the smallest number by which 1152 must be divided so that it becomes a perfect square. Also, find the square root of the number so obtained.

The product of two numbers is 1296. If one number is 16 times the other, find the numbers.

A welfare association collected Rs 202500 as donation from the residents. If each paid as many rupees as there were residents, find the number of residents.

A society collected Rs 92.16. Each member collected as many paise as there were members. How many members were there and how much did each contribute? 

A school collected Rs 2304 as fees from its students. If each student paid as many paise as there were students in the school, how many students were there in the school? 

Express each of the following product as a monomials and verify the result in each case for x = 1:
(4x²) × (−3x) × \[\left( \frac{4}{5} x^3 \right)\]

Express each of the following product as a monomials and verify the result in each case for x = 1:
(5x⁴) × (x²)³ × (2x)²

The area of a square field is 5184 cm². A rectangular field, whose length is twice its breadth has its perimeter equal to the perimeter of the square field. Find the area of the rectangular field.

Find the least square number, exactly divisible by each one of the numbers:
(i) 6, 9, 15 and 20

Find the least square number, exactly divisible by each one of the number: 

8, 12, 15 and 20

Express each of the following product as a monomials and verify the result in each case for x = 1:
(x²)³ × (2x) × (−4x) × (5)

Find the square roots of 121 and 169 by the method of repeated subtraction. 

Write down the product of −8x²y⁶ and −20xy. Verify the product for x = 2.5, y = 1.

Write the prime factorization of the following number and hence find their square root. 

 7744

Evaluate (3.2x⁶y³) × (2.1x²y²) when x = 1 and y = 0.5.