AP Board 8th Class Maths Solutions Chapter 6 Square Roots and Cube Roots Ex 6.4

AP State Syllabus AP Board 8th Class Maths Solutions Chapter 6 Square Roots and Cube Roots Ex 6.4 Textbook Questions and Answers.

AP State Syllabus 8th Class Maths Solutions 6th Lesson Square Roots and Cube Roots Exercise 6.4

Question 1.
Find the cubes of the following numbers
(1) 8
(ii) 16
(iii) 21
(iv) 30
Solution:

Number	Cube Of a Number
i) 8	8³ = 8 × 8 × 8 = 512
ii) 16	16³= 16 × 16 × 16 = 4096
iii) 21	21³ = 21 × 21 × 21 = 9261
iv) 30	30³ = 30 × 30 × 30 = 27000

Question 2.
Test whether the given numbers are perfect cubes or not.
(i) 243
(ii) 516
(iii) 729
(iv) 8000
(v)2700
Solution:

Number	Cube Of a Number	Yes / No
i) 243	3 × 3 × 3 × 3 × 3 = 3⁵	No
ii) 516	2 × 2 × 3 × 43	No
iii) 729	9 × 9 × 9 = 9³	Yes
iv) 8000	20 × 20 × 20 = (20)³	Yes
v) 2700	(30) × (30) × 3	No

Question 3.
Find the smallest number by which 8788 must be multiplied to obtain a perfect cube?
Solution:
The prime factorisation of 8788
= (2 × 2) × (13 × 13 × 13)
AP Board 8th Class Maths Solutions Chapter 6 Square Roots and Cube Roots Ex 6.4 1
∴ From the above product 2 ¡s left in the triplet.
∴ 2 should be multiplied with 8788 we will get a perfect cube number.

Question 4.
What smallest number should 7803 be multiplied with so that the product becomes a perfect cube?
Solution:
The prime factorisation of 7803
= (3 × 3 × 3) × (17 × 17)
AP Board 8th Class Maths Solutions Chapter 6 Square Roots and Cube Roots Ex 6.4 2
∴ From the above product 17 is left in
the triplet.
∴ 17 should be multiplied to 7803 then we will get a perfect cube number.

Question 5.
Find the smallest number by which 8640 must be divided so that the quotient is a perfect cube’?
Solution:
The prime factorisation of 8640
= (2 × 2 × 2) × (2 × 2 × 2) × 5 × (3 × 3 × 3)
= (2)³ × (2)³ × 5 × (3)³
AP Board 8th Class Maths Solutions Chapter 6 Square Roots and Cube Roots Ex 6.4 3

Question 6.
Ravi made a cuboid of plasticine ofdimensions 12cm, 8cm and 3cm. How many minimum number of such cuboids will be needed to form a cube’?
Solution:
The volume of a plasticine cuboid
= l × b × h
= 12 × 8 × 3
= 288 cm³
If the minimum no. of such cuboids will be needed to form a cube then its volume be less than 288 i.e., 216 cm³
∴ s³ = 216
s = \(\sqrt[3]{216}=\sqrt[3]{6 \times 6 \times 6}=\sqrt[3]{6^{3}}\) = 6
∴ The side of the cube 6 cm

Question 7.
Find the smallest prime number dividing the sum 3¹¹ +5¹³.
Solution:
The units digit in 3¹¹ is 7
AP Board 8th Class Maths Solutions Chapter 6 Square Roots and Cube Roots Ex 6.4 4
∴ The units digit in 3¹¹ is 7
The units digit in 5¹³ is 5
7 + 5 = 12 is divided by a smallest prime number 2.
∴ The smallest prime number that divide the sum 311 + 513 = 2