13. By which of the following numbers 600 has to be multiplied so that it becomes a perfect square?
a. 2
b. 3
c. 5
d. 6
Answer: D
$600 = {2^3} \times 3 \times {5^2}$
The powers of perfect squares are even numbers.
So 600 has to be multiplied with $2 \times 3$ so that it becomes ${2^4} \times {3^2} \times {5^2} = 3600$ which is ${60^2}$
14. By which of the following numbers 600 has to be multiplied so that it becomes a perfect cube?
a. 9
b. 15
c. 45
d. 90
Answer: C
Explanation:
$600 = {2^3} \times 3 \times {5^2}$
The powers of perfect cubes are multiples of 3.
So 600 has to be multiplied with ${3^2} \times 5$ so that it becomes ${2^3} \times {3^3} \times {5^3}$ = ${30^3}$
15. By what least number $3240$ has to be divided so that it becomes a perfect square?
a. 2
b. 5
c. 10
d. 15
Answer: C
Explanation:
$3240 = {2^3} \times {3^4} \times {5^1}$
So it has to be divisibly by $2 \times 5$ so that its powers become even numbers.
16. By what least number $3240$ has to be divisible so that it becomes a perfect cube?
a. 2
b. 5
c. 10
d. 15
Answer: D
Explanation:
$3240 = {2^3} \times {3^4} \times {5^1}$
So it has to be divisibly by $3 \times 5$ so that its powers become multiples of 3.
17. $1.\overline {234} = $
a. $\dfrac{{137}}{{111}}$
b. $\dfrac{{684}}{{555}}$
c. $\dfrac{{138}}{{111}}$
d. $\dfrac{{139}}{{111}}$
