Exercise 4
Question 1
Find the cubes of the following numbers :
(i) 13
(ii) 400
(iii) $\frac{-4}{9}$
(iv) $2 \frac{5}{7}$
(v) 0.3
(vi) 0.08
(vii) -2.4
(viii) 0.001
Sol :
Question 2
Which of the following numbers are perfect cubes ?
64,125,243,729,1331,864,4096,74088
Sol :
Sol :
Question 3
What is the smallest number by which 675 should be multiplied so that the product is a perfect cube ?
Sol :
Question 4
What is the smallest number by which 2916 should be divided so that the quotient is a perfect cube ?
Sol :
Question 5
Write cubes of five natural numbers which are multiples of 3 and verify the following :
'The cube of a natural number which is a multiple of 3 is a multiple of 27 '.
Sol :
Question 6
Find the cube roots of the following numbers by prime factorisation method :
(i) 125
(ii) 343
(iii) 2744
(iv) 3375
(v) $-729$
(vi) $-1728$
(vii) $\frac{-3375}{4913}$
(viii) $5 \frac{23}{64}$
Sol :
Question 7
Evaluate :
(i) $\sqrt[3]{0.216}$
(ii) $\sqrt[3]{4.096}$
(iii) $\sqrt[3]{0.003375}$
Sol :
Question 8
Show that $\sqrt[3]{27} \times \sqrt[3]{125}=\sqrt[3]{27 \times 125}$.
Sol :
Question 9
Find the value of
(i) $\sqrt[3]{392} \times \sqrt[3]{448}$
(ii) $\sqrt[3]{3375 \times 729}$
Sol :
Question 10
Find the smallest number by which 17496 must be divided, so that the quotient is a perfect cube. Also find the cube root of the quotient.
Sol :
Multiple Choice Questions (MCQs)
Question 11
The digit in the units place of the cube of 47 is :
(a) 9
(b) 7
(c) 3
(d) 1
Sol :
Question 12
The least possible value of A for which 90×A is a perfect cube is
(a) 200
(b) 300
(c) 500
(d) 600
Sol :
Question 13
$\sqrt[3]{5-\frac{10}{27}}$ is
(a) $\frac{4}{3}$
(b) $\frac{3}{4}$
(c) $\frac{5}{3}$
(d) $\frac{3}{5}$
Sol :
Question 14
$\sqrt[3]{-1728}+\sqrt{324}=$
(a) 30
(b) 6
(c) 4
(d) 32
Sol :
High Order Thinking Skills (HOTS)
Question 15
Evaluate : $\sqrt[3]{\sqrt{0.000729}}+\sqrt[3]{0.008}$
Sol :
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