Problem 1 :
Find the value of following cube roots:
x = ∛(27 × 2744)
Solution :
x = ∛(27 × 2744)
x = ∛(3 x 3 x 3 × 2 x 2 x 2 x 7 x 7 x 7)
x = 3 x 2 x 7
x = 42
Problem 2 :
Evaluate
Solution :
Problem 3 :
Two numbers 4x and 5x are such that sum of their cubes is 189. Find x.
Solution :
Sum of their cubes = 189
(4x)^{3} + (5x)^{3} = 189
64x^{3 }+ 125x^{3} = 189
189 x^{3} = 189
x^{3} = 189/189
x^{3} = 1
x = 1
Problem 4 :
The volume of a cube is 5832 m^{3}, find the length of the side.
Solution :
Volume of cube = 5832 m^{3}
a^{3} = 5832
a = ∛5832
a = ∛(2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3)
a = 2 x 3 x 3
a = 18
So, side length of cube is 18 m.
Problem 5 :
Three numbers are in the ratio 3 : 4 : 5. If the sum of their cubes -1728, find the three numbers.
Solution :
Let the three sides be 3x, 4x and 5x.
Sum of their cubes = -1728
(3x)^{3} + (4x)^{3} + (5x)^{3} = -1728
(27+64+125)x^{3 }= -1728
216x^{3 }= -1728
x^{3 }= -1728/216
x^{3 }= -8
x = -2
Problem 6 :
Check whether 648 is a perfect cube or not.
Solution :
Decomposing 648,
648 = 2 x 2 x 2 x 3 x 3 x 3 x 3
We see three 2's, three 3's. There is one more 3 not grouped.
So, the given number is not a perfect cube.
Problem 7 :
Three numbers are to one another as 2:3:4. The sum of their cubes is 33957. Find the numbers.
Solution :
Let the three numbers be 2x, 3x and 4x
(2x)^{3} + (3x)^{3} + (4x)^{3} = 33957
(8 + 27 + 64)x^{3} = 33957
99x^{3} = 33957
x^{3} = 33957/99
x^{3} = 343
x = 7
2x ==> 2(7) ==> 14
3x ==> 3(7) ==> 21
4x ==> 4(7) ==> 28
So, the three numbers are 14, 21 and 28.
Problem 8 :
Solution :
Problem 9 :
If y = 5, then what is the value of 10y√(y^{3} - y^{2}) ?
Solution :
= 10y√(y^{3} - y^{2})
By applying the value of y, we get
= 10(5)√(5^{3} - 5^{2})
= 50√(125 - 25)
= 50√100
= 50 (10)
= 500
Problem 10 :
Solution :
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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