Edudel, Directorate of Education Govt. of NCT of Delhi Class 8 Mental Maths Question Bank Chapter 7 Cube and Cube Roots Questions Solution. In this chapter, there is total 50 math problems. We have given each questions solution step by step.
Edudel Class 8 Mental Maths Chapter 7 Cube and Cube Roots:
1.) If x = 3√10/0.27 find x + 2/3
ANSWER:
Given that, x = 3√ 10/0.27
We have to find x + 2/3
3√ 10/0.27 we write this as 3√ 1000/27
3√ 10/0.27 = ((10 / 3) 3) 1/3
x =3√ 10/0.27 =10 / 3
x + 2/3 = 10 / 3 + 2/3
x + 2/3 = 4
2.) Find the value of3√ 1024/54
ANSWER:
We have to find,3√1024/54
After dividing by 2 we get,
3√1024/54= 3√512/27
We know,
3√ 512 = 8
3√27= 3
3√512/27 = ((8/3) 3) 1/3
3√1024/54 = 8/3
3.) Simplify: 3√512/125
ANSWER:
3√512/125
After simplifying we get,
We know,
3√ 512 = 8
3√125 = 5
3√512/125 = 8/5
4.) Find the smallest natural number other than 1, which is a perfect square as well as perfect cube.
ANSWER:
The smallest natural number other than 1, which is a perfect square as well as perfect cube is 64.
5.) Find the maximum number of digits in the cube of 4-digit number.
ANSWER:
The maximum number of digits in the cube of 4-digit number is 12.
6.) Find the minimum number of digit in the cube of a three-digit number.
ANSWER:
The minimum number of digit in the cube of a three-digit number is 7.
7.) If 64b = b4 then find the value of b2
ANSWER:
Given, 64b = b4
64b = b4/ b
64 = b3
We know,
3√64 = 4
64 = 43
b = 4
we have to find b2
b2 = 42 = 16
8.) Evaluate 0.33 – 0.23
ANSWER:
0.33 – 0.23
We use identity. a3 – b3 = (a-b) (a2 + b2 + ab)
We put a = 0.3 and b = 0.2
0.33 – 0.23 = (0.3-0.2) (0.32 + 0.22 + 0.3 x 0.2)
0.33 – 0.23 = 0.1 x (0.9 + 0.4 + 0.06)
0.33 – 0.23 = 0.019
9.) Write the unit’s digit of3√216×1728
ANSWER:
3√216×1728
We have to find the unit’s digit of3√216×1728
3√216×1728, here unit digit of 216 is 6
unit digit of 1728 is 8
6 x 8 = 48
We get unit digit of cube root 3√216×1728 is 8.
We know,
if a number has 8 at one’s place then its cube has 2 at one’s place.
The unit’s digit of 3√216×1728 is 2.
10.) If, 216x = 36 then find x.
ANSWER:
216x = 36
We know,
216 = 63
36 = 62
We put in equation.
63x = 62
After comparing,
3x = 2
X = 2/3
11.) Evaluate (3/5)3 – (2/5)3
ANSWER:
We have to find (3/5)3 – (2/5)3
We use identity. a3 – b3 = (a-b) (a2 + b2 + ab)
We put a =3/5 and b = 2/5
3/53 –2/53 = (3/5-2/5) (3/52 + 2/52 + 3/5 x2/5)
3/53 –2/53 = 1/5 x (9/25 + 4/25 + 6/25)
3/53 –2/53 = 1/5 x (19 /25)
3/53 –2/53 =19 /125
12.) Simplify:3√343×64
ANSWER:
We have to find3√343×64
We know,
3√343= 7
3√64= 4
3√343×64= 7 x 4 = 28
3√343×64 = 28
13.) Simplify:3√-50x40x4
ANSWER:
We have to find3√-50x40x4
-50 x 40 x 4 = -8000
3√8000= -20
3√-50x40x4 = -20
14.) Simplify: 331 + 331 + 331
ANSWER:
We have to find 331 + 331 + 331
After solving we get,
331 + 331 + 331 = 332
15.) Simplify: 732 x 7-34 x 74
ANSWER:
We have to find 732 x 7-34 x 74
We know rule of indices.
When base is same we add indices.
7(32 -34 + 4) = 72
72 = 49
17.) Evaluate 3√2x2x2x21x7x7x6x3
ANSWER:
We have to find 3√2x2x2x21x7x7x6x3
We know,
21 = 7 x 3
6 = 2 x 3
3√2x2x2x7x7x7x3x3x3= 2 x 7 x 3
3√2x2x2x21x7x7x6x3= 42
18.) Volume of a cube is 729 cm3. Then find the area of its face.
ANSWER:
Given that,
Volume of a cube is 729 cm3
We know,
Volume of a cube = (Side) 3
729 cm3= (Side) 3
We know,
3√729= 9
Side of cube = 9 cm.
The area of face of cube = (Side) 2
The area of face of cube = 92
The area of face of cube = 81.
19.) Evaluate3√ (0.01/17.28)
ANSWER:
We have to find 3√(0.01/17.28)
3√(0.01/17.28) = 3√1/1728
We know,
3√1728= 12
3√ (0.01/17.28) = 1/12
20.) Evaluate {500 + (104) ¼}3
ANSWER:
We have to find {500 + (104) ¼}3
We know,
Any number having indices 0 answer is 1.
500= 1
{1 + + (104) ¼}3
(11)3
{500 + (104) ¼}3 = 1331
21.) Evaluate {(242 +72)1/2}3
ANSWER:
We have to find {(242 +72)1/2}3
{(24 + 7)2)1/2}3
{(312)1/2}3
= 31 3
{(242 +72)1/2}3 = 15625
22.) The figure shows a cuboid with volume 1800 cm3. Find the value of x.
ANSWER:
Given that, cuboid with volume 1800 cm3
We know,
Volume of cuboid = Length x Breadth x Height
Volume of cuboid = (x + 3) x 3 x 6
1800 cm3 = (x + 3) x 18
(x + 3) = 1800 cm3 / 18
(x + 3) = 100
X = 97
23.) Find the smallest number that can be expressed in two different ways as sum of two different cubes. What is the special name given to such numbers?
ANSWER:
The numbers which can be expressed as the sum of two cubes in two different ways is called as Hardy-Ramanujan numbers.
the smallest number that can be expressed in two different ways as sum of two different cubes is 1729.
24.) Find the largest negative number which is a perfect cube.
ANSWER:
The largest negative number which is a perfect cube is -1.
- If 392 =2 x 2 x 2 x 7 x 7, 28=2× 2 x 7, and 81 = 3 x 3 x 3 x 3 find the least number by which 392 x 28 x 81 should be multiplied to get a perfect cube.
ANSWER:
Here, we have to find LCM of392 x 28 x 81 to get perfect cube.
We have to make group of 3 factors and take 1 from it.
Here, only 3 factors of 2 and 3 we get. And one 3 is remaining.
The least number by which 392 x 28 x 81 should be multiplied to get a perfect cube = 2 x 3 x 3
The least number by which 392 x 28 x 81 should be multiplied to get a perfect cube is 18.
26.) Area of one face of a cube is 121 cm2. Find the volume of the cube.
ANSWER:
Given that,
Area of one face of a cube is 121 cm2
The area of face of cube = (Side) 2
121 cm2= 112
Side of cube = 11 cm.
Now,
Volume of a cube = (Side) 3
Volume of a cube = (Side) 3
Volume of a cube = (11) 3
Volume of a cube = 1331 cm3
27.) Find the value of 203 – 173 if 202 + 172 + 20 x 17=1029.
ANSWER:
Given that,
202 + 172 + 20 x 17=1029
We have to find 203 – 173
We use identity. a3 – b3 = (a-b) (a2 + b2 + ab)
We put a =20 and b = 17
203 – 173= (20-17) (202 +172 + 20×17)
203 – 173= 3 x 1029
203 – 173= 3087
28.) Find the value of 133 + 173if 132 + 172 – 13 x 17 = 237
ANSWER:
Given that,
132 + 172 – 13 x 17 = 237
We have to find 133 + 173
We use identity. a3 + b3 = (a+b) (a2 + b2 – ab)
We put a =13 and b = 17
133 + 173 = (13 +17) (13 + 17–13 x 17)
133 + 173 = 30 x 237
133 + 173 = 7110
29.) Find the unit digit of 53273
ANSWER:
We have to find unit digit of 53273
5327= the unit digit is 7.
Cube of 7 = 73 = 343
We get 3 as a unit digit.
The unit digit of 53273is 3.
30.) Evaluate3√(40000/512) / 3√(5/512)
ANSWER:
We have to find3√(40000/512) / 3√(5/512)
3√40000/512 x 3√512/5
After solving,
3√8000= 20
3√(40000/512) / ∛(5/512)= 20
31.) Find the number of unit cubes in the given figure.
ANSWER:
We have to find the number of unit cubes.
Volume of cube = 5 x 3 x 4
Volume of Unit cube = 1 x 1 x 1
The number of unit cubes = Volume of cube / Volume of Unit cube
The number of unit cubes = 5 x 3 x 4 / 1 x 1 x 1
The number of unit cubes = 60
32.) How many cubes of edges 4 cm will be obtained on melting a solid of edge 12 cm?
ANSWER:
Volume of cube of edge 12 = 12 x 12 x 12
Volume of cube of edge 4 = 4 x 4 x 4
The number of cubes of edge 4 = 12 x 12 x 12 / 4 x 4 x 4
The number of cubes of edge 4 = 3 x 3 x 3.
The number of cubes of edge 4 = 27
33.) Find the volume of a cube of edge 12cm.
ANSWER:
We have to find volume of a cube of edge 12cm.
We know,
Volume of a cube = (side) 3
Volume of cube of edge 12 = 12 x 12 x 12
Volume of cube of edge 12 = 1728
34.) Find the cube root of 46656.
ANSWER:
We have to find cube root of 46656.
When the number having 6 at unit place then the same digit at one’s place.
∛46656= 36
The cube root of 46656 is 36.
35.) The volume of a cube is 9261000 m3. Find the edge of the cube.
ANSWER:
Given that,
The volume of a cube is 9261000 m3.
We know,
Volume of a cube = (Side) 3
9261000 m3.= (Side) 3
We know,
3√9261000= 210
Edge of cube = 210 m.
36.) Find the cube root of (-1728) × 125.
ANSWER:
We have to find cube root of (-1728) × 125.
We know,
3√-1728= -12
Also
3√125 = 5
Cube root of (-1728) × 125 = -12 x 5
Cube root of (-1728) × 125 = -60
37.) Find the number of thousand in 24 x 24 x 54
ANSWER:
We have to find 24 x 24 x 54
We know,
24= 2 x 2 x 2 x 2 = 16
54= 5 x 5 x 5 x 5 = 625
24x 54= 16 x 625 = 10 thousand
24 x 10 thousand = 240 thousand
38.) Find the number of hundreds in 14 x 24 x 52
ANSWER:
We have to find 14 x 24 x 52
We know,
24= 2 x 2 x 2 x 2 = 16
52= 5 x 5 = 25
24x 52 =400 = 4 Hundred
14x 4 Hundred = 56 Hundred
14 x 24 x 52 = 56 Hundred
39.) Two cubes have their volumes in the ratio 1:8. If the volume of smaller cube is 125 cubic cm. Find the side of another cube.
ANSWER:
Given that,
Two cubes have their volumes in the ratio 1:8.
The volume of smaller cube is 125 cubic cm.
1 ratio = 125 cubic cm.
8 ratio = ?
By cross Multiplication,
Volume of Larger cube = 125 x 8 = 1000 cm3
We know,
Volume of a cube = (Side) 3
1000 cm3= (Side) 3
We know,
3√1000 = 10
Side of cube = 10 cm.
40.) Simplify3√729/125
ANSWER:
We have to find3√729/125
By solving we get,
3√729/125= 9 / 5
41.) Evaluate 103 – 903
ANSWER:
We have to find 103 – 903
We use identity. a3 – b3 = (a-b) (a2 + b2 + ab)
We put a =10 and b = 9
103 – 903= (10-9) (102 +92 + 10 x 9)
103 – 903= 1 x (100 + 81 + 90)
103 – 903= 271
42.) Evaluate3√15624+3√0.08+3√0.008
ANSWER:
We have to find3√ 15624+3√ 0.08+3√ 0.008
We solve from innermost cube root.
We know,
3√0.008= 0.2
3√0.8+0.2= 3√1 = 1
3√15624+1
= 3√15625
3√15625 = 25
43.) How many consecutive odd numbers will be needed to obtain the sum as 53
ANSWER:
We know,
53= 125
2 consecutive odd numbers will be needed to obtain the sum as 53
44.) Find x if 72x-1 = 343
ANSWER:
We have to find 72x-1 = 343
We know,
343 = 73
72x-1 = 73
After comparing,
2x -1 = 3
2x = 3 + 1
2x = 4
X = 2
45.) Evaluate :[(122+162)/] 3
ANSWER:
We have to find :[(122+162)/] 3
:[( 144 + 256)/] 3
:[( 400)/] 3
(20) 3
:[(122+162)/] 3= 8000
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