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Published on: 03/10/2019
Cubes and Cube Roots
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Questions + Answers key
Take MCQ Mathematics Test
1.
What is the smallest number by which 648 must be multiplied so that the product is a perfect cube?
2.
Show that 384 is not a perfect cube
3.
Find the cube root of 2197.
4.
Find the smallest number by which 704 must be divided to obtain a perfect cube.
5.
Show that 46656 is a perfect cube.
6.
Which of the following are perfect cube?
i) 8000
ii)9000
7.
Is 42592 a perfect cube? If not, then by which smallest number should 42592 be divided so that quotient is a perfect cube?
8.
Find the cube root of 17576 through estimation
9.
Show that 0.001728 is the cube of a rational number. Find that rational number whose cube is 0.0017288.
10.
Find the sum of cubes of first four natural numbers.
1.
64cm3
2.
30
3.
9
4.
13
5.
11
6.
8000
7.
4
8.
The given number is 17576.
Step 1 Form groups of three starting from the rightmost digit of 17576.
17 576. In this case one group i.e., 576 has three digits whereas 17 has only two digits.
Step 2 Take 576.
The digit 6 is at its one’s place.
We take the one’s place of the required cube root as 6.
Step 3 Take the other group, i.e., 17.
Cube of 2 is 8 and cube of 3 is 27. 17 lies between 8 and 27.
The smaller number among 2 and 3 is 2.
The one’s place of 2 is 2 itself. Take 2 as ten’s place of the cube root of 17576.
Thus, \(\sqrt[3]{17576}\) = 26
9.
We have 0.001728 =\(1728\over1000000\)
Now,
\(\therefore {1728\over 1000000}\)
\(={2\times2\times2\times2\times2\times2\times3\times3\times3\over2\times2\times2\times2\times2\times2\times5\times5\times5\times5\times5\times5 }\)
\(={3\times3\times3\over 5\times5\times5\times5\times5\times5}={3^3\over 5^5\times5^3}=({3\over5\times5})^3\)
\(\therefore \sqrt[3]{1728\over 1000000}=({3\over 5\times5})^3\Rightarrow \sqrt[3]{1728\over 1000000}\)
\(={3\over 5\times5}\Rightarrow \sqrt[3]{0.001728}={3\over25}\)
Thus, 0.001728 is the cube of\({3\over25}\) .
10.
100
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