ML Aggarwal Cubes and Cube Roots Check Your Progress Class 8 ICSE Ch-4 Maths Solutions

ML Aggarwal Cubes and Cube Roots Check Your Progress Class 8 ICSE Ch-4 Maths Solutions. We Provide Step by Step Answer of  Check Your Progress Questions for Cubes and Cube Roots as council prescribe guideline for upcoming board exam. Visit official Website CISCE for detail information about ICSE Board Class-8.

ML Aggarwal Cubes and Cube Roots Check Your Progress Class 8 ICSE Maths Solutions

Board	ICSE
Publications	Avichal Publishig Company (APC)
Subject	Maths
Class	8th
Chapter-4	Cubes and Cube Roots
Writer	ML Aggarwal
Book Name	Understanding
Topics	Solution of Check Your Progress
Edition	2023-2024

Cubes and Cube Roots Check Your Progress

ML Aggarwal Class 8 ICSE Maths Solutions

Page-78

Question 1. Show that each of the following numbers is a perfect cube. Also, find the number whose cube is the given number:

(i) 74088
(ii) 15625

Answer:

(i) 74088

= 2 × 2 × 2 × 3 × 3 × 3 × 7 × 7 × 7

And, after grouping the same kind of prime factors in 3’s, its seen that no factor has been left ungrouped.

74088 = (2 × 2 × 2) × (3 × 3 × 3) × (7 × 7 × 7)

74088 is a perfect cube and its cube root is 2 × 3 × 7 = 42.

(ii) 15625

= 5 × 5 × 5 × 5 × 5 × 5

And, after grouping the same kind of prime factors, its seen that no factor is left ungrouped.

15625 = (5 × 5 × 5) × (5 × 5 × 5)

15625 is a perfect cube and its cube root is 5 × 5 = 25.

Question 2. Find the cube of the following numbers:

(i) -17
(ii) −3 (4/9)

Answer:

(i) Cube of -17

= (-17) × (-17) × (-17)

= -4913

(ii) Cube of  −3 (4/9)

= -31/9 is

= (-31/9) x (-31/9) x (-31/9)

= -29791/729

= -40(631/729)

Question 3. Find the cube root of each of the following numbers by prime factorisation:

(i) 59319
(ii) 21952

Answer:

(i) Cube root of 59319

(ii) Cube root of 21952

Question 4. Find the cube root of each of the following numbers:

(i) -9261
(ii) 2 (43/343)
(iii) 0.216

Answer:

(i) -9261

= -3 x 7 = -21

Question 5. Find the smallest number by which 5184 should be multiplied so that product is a perfect cube. Also find the cube root of the product.

Answer:

5184 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3

After grouping the same kind of prime factors is 3’s, its seen that one factor 3 is left ungroup.

5184 = (2 × 2 × 2) × (2 × 2 × 2) × (3 × 3 × 3) × 3

So, in order to complete it in 3’s, we must multiply the factors 3 × 3 i.e. equal to 9.

Thus, the required smallest number that should be multiplied to 5184 so that product is a perfect cube is 9.

The cube root of 5184 × 9 = 46656 is

= 2 × 2 × 3 × 3 = 36.

Question 6. Find the smallest number by which 8788 should be divided so that quotient is a perfect cube. Also, find the cube root of the quotient.

Answer:

8788 = 2 × 2 × 13 × 13 × 13

On grouping of the same kind of factors, it’s seen that 2 × 2 has been left ungrouping.

8788 = 2 × 2 × (13 × 13 × 13)

So, 2 × 2 = 4 is the least number by which 8788 should be divided so that quotient is a perfect cube.

Hence, 8788 ÷ 4 = 2197 and its cube root = 13.

Question 7. Find the side of a cube whose volume is 4096 m³.

Answer:

Volume of a cube = 4096 m³

Hence, the side of the cube is 16 m.

—  : End of ML Aggarwal Check Your Progress Class 8 ICSE Maths Solutions :–

Return to –  ML Aggarwal Maths Solutions for ICSE Class -8

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