Cubes and Cube Roots - Class 8 Mathematics - Chapter 6 - Notes, NCERT Solutions & Extra Questions
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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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Is 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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Is 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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Is 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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Find the cube root of 8000.
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Find the cube root of 13824 by prime factorisation method.
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Ask Chatterbot AIExercise 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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Find 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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Parikshit 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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Ask Chatterbot AIExercise 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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Ask Chatterbot AIExtra 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
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6: If two positive integers $a$ and $b$ are written as $a=x^{3} y^{2}$ and $b=x y^{2}$ where $x,y$ are prime numbers, then $\operatorname{HCF}(a, b)$ is
A) $xy$
B) $xy^{2}$
C) $x^{3}y^{3}$
D) $x^{2}y^{2}$
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If two roots of the equation $x^{3} - 3x + 2 = 0$ are the same, then the roots will be
(A) $2, 2, 3$ (B) $1, 1, -2$ (C) $-2, 3, 3$ (D) $-2, -2, 1$
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16 can be expressed as:
(A) $2 \times 2 \times 2$ (B) $2 \times 2 \times 2 \times 2$ (C) $2 \times 2 \times 2 \times 2 \times 2$ (D) $2 \times 3 \times 3$
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$(99)^{2}$ is equivalent to
A) 9001
B) 8801
C) 9881
D) 9801
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The length of the longest rod that can fit in a cubical vessel of side $10$ cm is (a) $10$ cm (b) $20$ cm (c) $10\sqrt{2}$ cm (d) $10\sqrt{3}$ cm
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Number of integers $k$ for which the equation $x^{3} - 27x + k = 0$ has at least two distinct integer roots is
A. 1
B. 2
C. 3
D. 4
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The value of $(107)^2 - (93)^2$ is:
A) 2800
B) $\mathbf{1008}$
C) $\mathbf{1382}$
D) 36482
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"The main directory of a disk is called $\qquad$ directory."
A) root
B) sub
C) folder
D) network
E) None of these
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The volume of a cube of side 'a' is
(A) $a \times a \times a$ (B) $a \times a$ (C) $3a$ (D) $a+3$
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If $a + \frac{1}{a} = 2\sqrt{3}$, then find the value of $a^{3} + \frac{1}{a^{3}}$.
A) 0
B) $18\sqrt{3}$
C) $9\sqrt{3}$
D) $\sqrt{3}$
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