Which of the following is a prime factor of 24?

• 1

• 2

• 4

• 6

Answer explanation

Any factor of the given number which is a prime number also is called prime factor of the number. In the given options, numbers, 1, 2, 4 and 6 all are factors of 24 but 1, 4 and 6 are not prime numbers only 2 is the prime number. Hence the prime factor of 24 among given options is 2

Tags

CCSS.4.OA.B.4

Using Prime factorisation method, find the value of √3136

• 56

• 79

• 85

• 45

Answer explanation

The prime factorisation of 3136 can be done as shown. So, 3136 = 2 x 2 x 2 x 2 x 2 x 2 x 7 x 7 Let's pair the similar prime factors 3136 = (2 x 2) x (2 x 2) x (2 x 2) x (7 x 7) So, √3136 = 2 x 2 x 2 x 7 = 56

What is the smallest perfect square divisible by 2, 3, 5 and 6?

• 32400

• 900

• 400

• 2356

Answer explanation

The smallest number divisible by 2, 3, 5 and 6 is LCM of these numbers. So, LCM of 2, 3, 5, 6 = 2 x 3 x 5 To find the smallest perfect square number divisible by these numbers we have to find the square of its the prime factors. So, smallest perfect square divisible by 2, 3, 5, and 6 = (2 x 2) x (3 x 3) x (5 x 5) = 900

Tags

CCSS.6.EE.A.1

The value of the given expression is

• 46

• 64

• 8

• Can not be determined

Answer explanation

√(19 + √2025) = √(19 + 45) = √64 = 8

Tags

CCSS.HSN.RN.A.2

A farmer planted 1444 plants in some rows and columns in such a way that there are as many plants in each column as there are in each row. What is the number of plants in a row?

• 19

• 1444

• 38

• 18

Answer explanation

According to given situation, the number of plants in a row = number of plants in a column. Total number of plants = number of plants in a row × number of plants in a column Let number of plants in a row = x then, Total number of plants = x² = 1444 i.e. x = √1444 Since, 1444 = 2 x 2 x 19 x 19 Hence, x = √1444 = 2 x 19 = 38 Thus there are 38 plants in each row.

A rectangle has length 24 cm and width 7 cm. The length of its diagonal is ____

• 625 cm

• 25 cm

• 5 cm

• 31 cm

Answer explanation

IF length of the rectangle is l, width of the rectangle is b and length of diagonal is c then they are related as c² = a² + b² So, c² = 24² + 7² c² = (24 x 24) + (7 x 7) = 576 + 49 c² = 625 i.e., c = √625 using prime factorisation we get c = √(5 x 5 x 5 x 5) i.e. c = 5 x 5 = 25 cm Hence length of the diagonal of the rectangle is 25 cm

Tags

CCSS.7.EE.B.3

Find the smallest perfect square number that is divisible by 3, 18 and 22.

• 4356

• 4365

• 198

• 66

Answer explanation

If we have to find the number that is divisible by 3, 18 and 22 then we need to find the least common multiple (LCM) of 3, 18 and 22. The LCM of 3, 18 and 22 = 198 The number 198 is not a perfect square number. We know that in the factorization of a perfect square number all the prime factors are in pairs. The prime factors of 198 are: 198 = 3 x 3 x 2 x 11 In this the number 2 and 11 are not in pairs. Hence we will multiply both sides by 2 and 11. So 198 x 2 x 11 = (3 x 3) x (2 x 2) x (11 x 11) 4356 = (3 x 3) x (2 x 2) x (11 x 11) 4356 = 3² x 2² x 11² 4356 = (3 x 2 x 11)² 4356 = 66² √4356= 66 Hence, 4356 is the smallest perfect square number that is divisible by 3, 18 and 22.

Tags

CCSS.6.EE.A.1