Students can Download Maths Chapter 5 Squares, Square Roots, Cubes, Cube Roots Ex 5.2 Questions and Answers, Notes Pdf, KSEEB Solutions for Class 8 Maths helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.

## Karnataka Board Class 8 Maths Chapter 5 Squares, Square Roots, Cubes, Cube Roots Ex 5.2

Question 1.

Find the sum 1 + 3 + 5 + _____ +51 (the sum fo all odd numbers from 1 to 51) without actually adding them.

Answer:

The sum of first n odd numbers is n^{2}

∴ 1 +3 + 5+ _____ + 51 = 26^{2} = 676.

Question 2.

Express 144 as a sum of 12 odd numbers.

Answer:

144 = 122 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23.

Question 3.

Find the 14^{th} and 15^{th} triangular numbers and find their sum verify the statement 8 for this sum.

Answer:

14 th triangular number =1 + 2 + 3+4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 = 105.

15 th triangular number = 1 + 2 + 3 + 4 + ___ + 15 = 120

Sum of 105 + 120 = 225

According to statement 8, the sum of 14th and 15th triangular numbers in equal to

n + (n + 1) = (n + 1)^{2}

105 + 120 = (14 + 1)^{2}

225 = 225.

Question 4.

What are the remainders of a perfect square when divided by 5?

Answer:

When perfect squares 9, 16, 25, 36, 49, 64 are divided by 5 the remainders are 4, 1, 0, 1, 4, 4 respectively.

Therefore the remainders of a perfect square when divided by 5 are 0, 1, and 4.