AP Board Class 8 Maths Chapter 6 Square Roots and Cube Roots Ex 6.5 Textbook Solutions PDF: Download Andhra Pradesh Board STD 8th Maths Chapter 6 Square Roots and Cube Roots Ex 6.5 Book Answers ~ HSSlive: Plus One & Plus Two Notes & Solutions for Kerala State Board

AP Board Class 8 Maths Chapter 6 Square Roots and Cube Roots Ex 6.5 Textbook Solutions PDF: Download Andhra Pradesh Board STD 8th Maths Chapter 6 Square Roots and Cube Roots Ex 6.5 Book Answers

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Andhra Pradesh Board Class 8th Maths Chapter 6 Square Roots and Cube Roots Ex 6.5 Textbooks Solutions PDF

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Andhra Pradesh State Board Class 8th Maths Chapter 6 Square Roots and Cube Roots Ex 6.5 Books Solutions

Board	AP Board
Materials	Textbook Solutions/Guide
Format	DOC/PDF
Class	8th
Subject	Maths
Chapters	Maths Chapter 6 Square Roots and Cube Roots Ex 6.5
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AP Board Class 8th Maths Chapter 6 Square Roots and Cube Roots Ex 6.5 Textbooks Solutions with Answer PDF Download

Find below the list of all AP Board Class 8th Maths Chapter 6 Square Roots and Cube Roots Ex 6.5 Textbook Solutions for PDF’s for you to download and prepare for the upcoming exams:

Question 1.
Find the cube root of the following numbers by prime factorization method.
(i) 343
(ii) 729
(iii) 1331
(iv) 2744
Solution:

Question 2.
Find the cube root of the following numbers through estimation’?
(i) 512
(ii) 2197
(iii) 3375
(iv) 5832
Solution:
Step 1: Start making groups of three digits starting from the unit place.
i.e, 512⎯⎯⎯⎯⎯⎯⎯⎯⎯ First group is 512

Step 2: First group i.e 512 will give us the units digit of the cube root. As 512 ends with 2, then its cube root ends with 8 (2 x 2 x 2) So the units place of the cube root will be 8.

Step 3: Now take the second group i.e. 0. Which is 0³ < 1 < 2³.
So the least number is ‘0′.
∴ Tens digit of a cube root of a number be 0.
∴ 512‾‾‾‾√3 = 08 = 8

(ii) 2197
Step 1: Start making groups of three digits starting from the unit place.

Step 2: First group i.e., 197 will give us the units digit of the cube root.
As 197 ends with 7, its cube root ends with 3. ‘
[∵ 3 x 3 x 3 = 27]
∴ Its units digit is 7.

Step 3: Now take the second group i.e.,2
We know that i3 < 2 < 2
∴ The least number be 1.
∴ The required number is 13.
∴ 2197‾‾‾‾‾√3=13×13×13‾‾‾‾‾‾‾‾‾‾‾‾√3=]√⧸(13)8
= 13

(iii) 3375
Step 1: Start making groups of three digits starting from the unit place.
i.e.;

Step 2: First group is 375. Its units digit is 5.
∴ The cube root is also ends with 5.
∴ The units place of the cube root will be 5.

Step 3: Now take the second group,
i.e., 3 we know that 1³ < 3³ <2³
∴ The least number is 1.
∴ The tens digit of a cube root will be 1.
∴ The required number = 15
3375‾‾‾‾‾√3=15×15×15‾‾‾‾‾‾‾‾‾‾‾‾√3=15⧸3‾‾‾‾√⧸=15

(iv) 5832
Step 1: Start making groups of three digits starting from the unit place.

Step 2: The units digit of 832 is 2.
∴ The cube root of the number ends with units digit 8.
[∵ 8 x 8 x 8 = 512]

Step 3: In the second group i.e., 5 lie between 1 and 6
i.e., 1³ < 5 < 2³
∴ The tens digit of a number will bel.
∴ The required number is 18.
∴ 5832‾‾‾‾‾√3=18×18×18‾‾‾‾‾‾‾‾‾‾‾‾√3=(18)3‾‾‾‾‾√3
= 18

Question 3.
State true or false?
(i) Cube of an even number is an odd number
(ii) A perfect cube may end with two zeros
(iii) If a number ends with 5, then its cube ends with 5
(iv) Cube of a number ending with zero has three zeros at its right
(v) The cube of a single digit number may be a single digit number.
(vi) There is no perfect cube which ends with 8
(vii) The cube of a two digit number may be a three digit number.
Solution:
(i) Cube of an even number is an odd number (F)
(ii) A perfect cube may end with two zeros (F)
(iii) If a number ends with 5, then its cube ends with 5. (T)
(iv) Cube of a number ending with zero has three zeros at its right. (T)
(v) The cube of a single digit number may be a single digit number. (F)
(vi) There is no perfect cube which ends with 8(F)
(vii) The cube of a two digit number may be a three digit number. (F)

Question 4.
Find the two digit number which is a square number and also a cubic number.
Solution:
The two digited square and cubic
number is 64
∴ 64 = 8 x 8 = 8² ⇒ 64‾‾‾√ = 8
64 = 4 x 4 x 4 = 4³ ⇒ 64‾‾‾√3 = 4

AP Board Textbook Solutions PDF for Class 8th Maths

Andhra Pradesh Board Class 8th Maths Chapter 6 Square Roots and Cube Roots Ex 6.5 Textbooks for Exam Preparations

Andhra Pradesh Board Class 8th Maths Chapter 6 Square Roots and Cube Roots Ex 6.5 Textbook Solutions can be of great help in your Andhra Pradesh Board Class 8th Maths Chapter 6 Square Roots and Cube Roots Ex 6.5 exam preparation. The AP Board STD 8th Maths Chapter 6 Square Roots and Cube Roots Ex 6.5 Textbooks study material, used with the English medium textbooks, can help you complete the entire Class 8th Maths Chapter 6 Square Roots and Cube Roots Ex 6.5 Books State Board syllabus with maximum efficiency.

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