The possible digit the ones place in the cube root of 9,70,299 is:
a) 3
b) 7
c) 9
d) 6
The smallest number by which 3072 has to be divided to make it a perfect cube is
a) 3
b) 4
c) 2
d) 6
The cube root of 8,30,584 is:
a) 92
b) 94
c) 96
d) 98
The number by which 40,000 should be divided to make it a perfect cube is:
a) 100
b) 40
c) 4
d) 100
Thevalueof is:
a) 20
b) 10
c) -10
d) 5
Answers with Explanation:
The possible digit the ones place in the cube root of 9,70,299 is:
Whenever this type of questions are asked then we have to only notice the unit/ones digit of the given number.
Here the unit digit of the given number is 9, so the possible digit at the ones place in the cube root of 9,70,299 is 9.
And this is because “unit digit of a cube number is the unit digit of its last digit.”
Verification: ( Not needed )
We can also verify it by finding its cube root.To find its cube root, we will resolve it into prime factors-
9 | 9,70,299
9 | 1,07,811
9 | 11,979
11 | 1,331
11 | 121
11 | 11
| 1
☞ 9,70,299 = 9 × 9 × 9 × 11 × 11 × 11
☞ = 9 × 11 = 99
Here, we can see that unit digit of cube root of 9,70,299 is 9. Then, hence verified!!!
_________________
The smallest number by which 3072 has to be divided to make it a perfect cube is:
To find the smallest number by which 3072 has to be divided to make it a perfect cube , we will resolve it into prime factors by by prime factorization-
Resolving 3072 into prime factors-
2 | 3072
2 | 1536
2 | 768
2 | 384
2 | 192
2 | 96
2 | 48
2 | 24
2 | 12
2 | 6
3 | 3
| 1
☞ 3072 = 2×2×2 × 2×2×2 × 2×2×2× 2 × 3
Clearly , to make 3072 a perfect cube, it must be divided by (2 × 3) = 6 Ans.
_____________
The cube root of 8,30,584 is:
To find the cube root of 8,30,584 , we will resolve it into prime factors,
Resolving 8,30,584 into prime factors, we get -
2 | 8,30,584
2 | 4,15,292
2 | 207646
47| 103823
47| 2209
47| 47
47| 1
☞ 8,30,584 = 2×2×2 × 47×47×47
☞ = 2 × 47 = 94 ( Answer) } [/tex]
_________________
The number by which 40,000 should be divided to make it a perfect cube is:
To find the number by which 40,000 should be divided to make it a perfect cube , we will resolve it into prime factors-
Resolving40,000intoprimefactors,weget -
2 | 40,000
2 | 20,000
10| 10,000
10| 1,000
10| 100
10| 10
| 1
☞ 40,000 = 2 × 2 × 10 × 10×10×10×10
Clearly , to make 40,000 a perfect cube, it must be divided by ( 2 × 2 × 10 ) = 40 ( Ans)
________________
The value ofis:
We can also write as because -25 × 40 is -1000.
Now to find the cube root of -1000, we will resolve it into prime factors-
Answers & Comments
Required Answers:
Answers with Explanation:
Here the unit digit of the given number is 9, so the possible digit at the ones place in the cube root of 9,70,299 is 9.
And this is because “unit digit of a cube number is the unit digit of its last digit.”
Verification: ( Not needed )
We can also verify it by finding its cube root.To find its cube root, we will resolve it into prime factors-
☞ 9,70,299 = 9 × 9 × 9 × 11 × 11 × 11
☞
= 9 × 11 = 99
Here, we can see that unit digit of cube root of 9,70,299 is 9. Then, hence verified!!!
_________________
To find the smallest number by which 3072 has to be divided to make it a perfect cube , we will resolve it into prime factors by by prime factorization-
Resolving 3072 into prime factors-
☞ 3072 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3
Clearly , to make 3072 a perfect cube, it must be divided by (2 × 3) = 6 Ans.
_____________
To find the cube root of 8,30,584 , we will resolve it into prime factors,
Resolving 8,30,584 into prime factors, we get -
☞ 8,30,584 = 2 × 2 × 2 × 47 × 47 × 47
☞
= 2 × 47 = 94 ( Answer) } [/tex]
_________________
To find the number by which 40,000 should be divided to make it a perfect cube , we will resolve it into prime factors-
Resolving 40,000 into prime factors, we get -
☞ 40,000 = 2 × 2 × 10 × 10 × 10 × 10 × 10
Clearly , to make 40,000 a perfect cube, it must be divided by ( 2 × 2 × 10 ) = 40 ( Ans)
________________
We can also write
as
because -25 × 40 is -1000.
Now to find the cube root of -1000, we will resolve it into prime factors-
Resolving -1000 into prime factors we get,