M l aggarwal understanding icse mathematics class 8 Solutions for Chapter 4 cubes and cube roots

Which of the following numbers are not perfect cubes? Give reasons in support of your answer:

(i) 648

(ii) 729

(iii) 8640

(iv) 8000

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

the given number:

(i) 1728

(ii) 5832

(iii) 13824

(iv) 35937

Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube:

(i) 243

(ii) 3072

(iii) 11979

(iv) 19652

Find the smallest number by which each of the following numbers must be divided to obtain a

perfect cube:

(i) 1536

(ii) 10985

(iii) 28672

(iv) 13718

Rahul makes a cuboid of plasticine of sides 3 cm × 3 cm × 5 cm. How many such cuboids will he

need to form a cube

Find the volume of a cubical box whose surface area is 486 cm2.

Which of the following are cubes of even natural numbers or odd natural numbers:

(i) 125

(ii) 512

(iii) 1000

(iv) 2197

(v) 4096

(vi) 6859

Write the one’s digit of the cube of each of the following numbers:

(i) 231

(ii) 358

(iii) 419

(iv) 725

(v) 854

(vi) 987

(vii) 752

(viii) 893

Find the cubes of the following numbers:

(i) -13

(ii) 3 \frac{1}{5} (iii) 5 \frac{1}{7}

Find the cube root of each of the following numbers by prime factorization:

(i) 12167

(ii) 35937

(iii) 42875

(iv) 21952

(v) 373248

(vi) 32768

(vii) 262144

(viii) 157464

Find the cube root of each of the following cube numbers through estimation.

(i) 19683

(ii) 59319

(iii) 85184

(iv) 148877

Find the cube root of each of the following numbers:

(i) -250047 (ii) -64/1331 (iii) (iv)

4 \frac{17}{27}, 5 \frac{1182}{2197}

4. Evaluate the following: (i) \sqrt[3]{512 \times 729} (i i) \sqrt[3]{(-1331) \times 3375}

Find the cube root of the following decimal numbers:

(i) 0.003375

(ii) 19.683

\sqrt[3]{27}+\sqrt[3]{0.008}+\sqrt[3]{0.064}

Multiply 6561 by the smallest number so that product is a perfect cube. Also, find the cube root of the product.

Divide the number 8748 by the smallest number so that the quotient is a perfect cube. Also, find the cube root of the quotient.

The volume of a cubical box is 21952 m3. Find the length of the side of the box

Three numbers are in the ratio 3: 4: 5. If their product is 480, find the numbers

Two numbers are in the ratio 4: 5. If the difference of their cubes is 61, find the numbers

The difference of two perfect cubes is 387. If the cube root of the greater of two numbers is 8, find the cube root of the smaller number

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

Find the cube of the following numbers:

(i) -17 (ii) -3 \frac{4}{9}

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

(i) 59319

(ii) 21952

Find the cube root of each of the following numbers:

(i) -9261

(ii) 2 \frac{43}{343} (iii) 0.216

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

Find the smallest number by which 8788 should be divided so that the quotient is a perfect cube.

Also, find the cube root of the quotient

Find the side of a cube whose volume is 4096 m3