Cubes and Cube Roots - Class 8 - Mathematics
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Examples - Cubes and Cube Roots | NCERT | Mathematics | Class 8
Is 243 a perfect cube?
No, $243$ is not a perfect cube. The nearest cubic numbers to $243$ are $216$ and $343$.
Here is a plot of the cubic numbers, showing how $243$ is not among them:
And here is a number line indicating the position of $243$ relative to nearby cubic numbers:
Is 392 a perfect cube? If not, find the smallest natural number by which 392 must be multiplied so that the product is a perfect cube.
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Sign up nowIs 53240 a perfect cube? If not, then by which smallest natural number should 53240 be divided so that the quotient is a perfect cube?
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Sign up nowIs 1188 a perfect cube? If not, by which smallest natural number should 1188 be divided so that the quotient is a perfect cube?
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Sign up nowIs 68600 a perfect cube? If not, find the smallest number by which 68600 must be multiplied to get a perfect cube.
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Sign up nowFind the cube root of 8000.
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Sign up nowFind the cube root of 13824 by prime factorisation method.
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Sign up nowExercise 6.1 - Cubes and Cube Roots | NCERT | Mathematics | Class 8
Which of the following numbers are not perfect cubes?
(i) 216
(ii) 128
(iii) 1000
(iv) 100
(v) 46656
The numbers that are not perfect cubes among the given options are:
- (ii) $128$
- (iv) $100$
The numbers that are perfect cubes are:
- (i) $216$ (it is the cube of $6$)
- (iii) $1000$ (it is the cube of $10$)
- (v) $46656$ (it is the cube of $36$)
Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.
(i) 243
(ii) 256
(iii) 72
(iv) 675
(v) 100
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Sign up nowFind the smallest number by which each of the following numbers must be divided to obtain a perfect cube.
(i) 81
(ii) 128
(iii) 135
(iv) 192
(v) 704
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Sign up nowParikshit makes a cuboid of plasticine of sides $5 \mathrm{~cm}, 2 \mathrm{~cm}, 5 \mathrm{~cm}$. How many such cuboids will he need to form a cube?
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Sign up nowExercise 6.2 - Cubes and Cube Roots | NCERT | Mathematics | Class 8
Find the cube root of each of the following numbers by prime factorisation method.
(i) 64
(ii) 512
(iii) 10648
(iv) 27000
(v) 15625
(vi) 13824
(ix) 175616
(x) 91125
(vii) 110592
(viii) 46656
State true or false.
(i) Cube of any odd number is even.
(ii) A perfect cube does not end with two zeros.
(iii) If square of a number ends with 5, then its cube ends with 25 .
(iv) There is no perfect cube which ends with 8 .
(v) The cube of a two digit number may be a three digit number.
(vi) The cube of a two digit number may have seven or more digits.
(vii) The cube of a single digit number may be a single digit number.
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Sign up nowExtra Questions - Cubes and Cube Roots | NCERT | Mathematics | Class 8
Find the cube root of:
(i) $343$
(ii) $1000$
(iii) $2744$
(iv) $74088$
Answer:
(i) To find the cube root of $343$, consider prime factors or perfect cubes known: $$ 343 = 7 \times 7 \times 7 = 7^3 $$ Therefore, the cube root is: $$ \sqrt[3]{343} = 7 $$
(ii) For $1000$, since it is a common cubic number, $$ 1000 = 10 \times 10 \times 10 = 10^3 $$ Thus, the cube root is: $$ \sqrt[3]{1000} = 10 $$
(iii) For $2744$, considering known cubes: $$ 2744 = 14 \times 14 \times 14 = 14^3 $$ Therefore, the cube root is: $$ \sqrt[3]{2744} = 14 $$
(iv) For $74088$, breaking down into its factors and recognizing perfect cubes: Hence, its cube root is: $$ \sqrt[3]{74088} = 2 \times 23 = 42 $$
Thus, the cube roots are:
7
10
14
42
Using prime factorization, find which of the following are perfect cubes.
a) 128
b) 343
c) 729
d) 1331
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Sign up now"There are 8 pipes which take 26 hours to fill a big drum. But when the operations were supposed to begin, two pipes were damaged. It so happened that only one could be retrieved back to a usable state. What will be the time taken to fill the drum with the existing pipes?"
A) 29.7 hours
B) 30.7 hours
C) 28.7 hours
D) 27.7 hours.
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Sign up nowWhich of the following is an example of a non-polyhedron?
A. Cube
B. Cone
C. Triangular prism
D. Triangular pyramid
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Sign up nowThe arrangement $A$ $B$ $C$ $\ldots$ $A$ $B$ $C$ $\ldots$ $A$ $B$ $C$ $\ldots$ is referred to as
A) octahedral close packing
B) hexagonal close packing
C) tetragonal close packing
D) cubic close packing
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Sign up now2000 cubic centimeters $=$ $\qquad$ cubic meters.
(A) 0.2
(B) 0.02
(C) 0.002
(D) 0.0002
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Sign up nowSimplify: $\frac{\sqrt[4024]{44}}{\sqrt[4]{4}}$
A) 4
B) 2
C) 16
D) 64
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Sign up nowFind the value of $\left(36^{3}\right)^{-3}$.
A) $\left(36^{-9}\right)$
B) $\left(36^{9}\right)$
C) $\left(6^{18}\right)$
D) $\left(6^{-18}\right)$
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Sign up now$\tan \frac{\pi}{3} = \sqrt{3}$
A) True
B) False
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Sign up now$(a + b)$ and $(a - b)$ are two diagonals of a rhombus; $a, b > 0$. What is the value of $a^{3} + b^{3}$, if the area of the rhombus is $30 , \mathrm{cm}^{2}$? Given that one of the diagonals is $6 , \mathrm{cm}$.
A) $60 , \mathrm{cm}$
B) $520 , \mathrm{cm}$
C) $504 , \mathrm{cm}$
D) $80 , \mathrm{cm}$
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Sign up nowTwo towers $A$ and $B$ are standing at some distance apart. From the top of tower $A$, the angle of depression of the foot of tower $B$ is found to be $30^\circ$. From the top of tower $B$, the angle of depression of the foot of tower $A$ is found to be $60^\circ$. If the height of tower $B$ is '$h$' meters, then the height of tower $A$ in terms of '$h$' is
(A) $2h$ meters (B) $\frac{h}{3}$ meters (C) $\sqrt{3} h$ meters (D) $\frac{h}{\sqrt{3}}$ meters
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Sign up nowThe value of $\cos^{3}\left(60^{\circ}-A\right)-\cos^{3}\left(60^{\circ}+A\right)$ is
(A) $3\sqrt{3}$
(B) $\frac{3\sqrt{3}}{4} \sin A$
(C) $\frac{3\sqrt{3}}{4}$
(D) $3\sqrt{3} \sin A$
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