Cube Root of a Negative Number
Category : 8th Class
The cube root of a negative number is always negative i.e. \[{{(-n)}^{\frac{1}{3}}}=-{{(n)}^{\frac{1}{3}}}\]
The cube root of -1000 is -10 because \[{{(-10)}^{3}}\]\[=-10\times -10\times -10=-1000\].
In symbolic form, the cube root of -1000 is written as \[\sqrt[3]{-1000}\]
So, \[\sqrt[3]{-1000}=-10\]
\[\because \]\[{{(-10)}^{3}}=-10\times -10\times -10=-1000\]
From the above, we can infer that:
Find the unit digit in the cube of the number 3331.
(a) 1
(b) 8
(c) 4
(d) 9
(e) None of these
Answer: (a)
Explanation:
We know that, \[{{\text{(3331)}}^{\text{3}}}=\text{3331}\times \text{3331}\times \text{3331}=\text{36959313691}\].
The smallest number by which 2560 must be multiplied so that the product will be a perfect cube.
(a) 35
(b) 25
(c) 8
(d) 5
(e) None of these
Answer: (b)
Explanation:
The factors of 2560 is given by
\[\text{256}0=\text{5}\times \text{8}\times \text{8}\times \text{8}\]
In this factors there are three 8 and one 5. So in order to make the number 5 perfect cube we have to multiply it by 25. Therefore, 25 is the least number by which it must be multiplied so that it becomes a perfect cube.
The smallest number by which we must divide 8788 so that it becomes a perfect cube.
(a) 2
(b) 169
(c) 4
(d) 13
(e) None of these
Answer: (c)
Find the value of \[{{\left[ {{({{5}^{2}}+{{12}^{2}})}^{\frac{1}{2}}} \right]}^{3}}\] is given by:
(a) 2197
(b) 169
(c) 1693
(d) 289
(e) None of these
Answer: (a)
Find the cube root of 42875.
(a) 35
(b) 25
(c) 15
(d) 20
(e) 32
Answer: (a)
Explanation:
The factors of \[\text{42875}=\text{5}\times \text{5}\times \text{5}\times \text{7}\times \text{7}\times \text{7}\]
\[\sqrt[3]{42874}=\sqrt[3]{\underline{5\times 5\times 5}\times \underline{7\times 7\times 7}}=5\times 7=35\]
Make the factors of number by taking three identical numbers. Now multiply each number of the factors.
Find the least number by which 3087 must be multiplied to make it a perfect cube.
(a) 3
(b) 4
(c) 9
(d) 7
(e) None of these
Answer: (a)
Exploration:
The factors of \[\text{3}0\text{87}=\text{3}\times \text{3}\times \text{7}\times \text{7}\times \text{7}\]
We note that the factor 3 appears only 2 times, so if we multiply 3087 by 3 we get \[3084\times 3={{(3)}^{3}}\times {{(7)}^{3}}={{(3\times 7)}^{3}}\], so the smallest number is 3 which when multiplied to 3087, it gives a perfect cube.
Find the cube root of \[\frac{-2197}{1331}\].
(a) \[\frac{-13}{11}\]
(b) \[\frac{13}{11}\]
(c) \[-\frac{13}{21}\]
(d) \[-\frac{17}{21}\]
(e) None of these
Answer: (a)
Find the value of \[\sqrt[3]{\frac{0.027}{0.008}}-\sqrt{\frac{0.09}{0.04}}-1\]
(a) 1
(b) -1
(c) 0
(d) \[\frac{3}{2}\]
(e) None of these
Answer: (b)
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