Squareroots & Cuberoots Model Questions Set 1 Practice Questions Answers Test with Solutions & More Shortcuts
Squareroots & Cuberoots PRACTICE TEST [1 - EXERCISES]
Squareroots & Cuberoots Model Questions Set 1
Question : 11
The square of a natural number when subtracted from its cube results in 48. The number is
a) 5
b) 6
c) 4
d) 8
Answer »Answer: (c)
Let the natural number be 'x'.
∴ $x^3-x^2$=48
⇒$x^2$(x-1)=48
⇒$4^2$(4-1)=48
∴ x= 4
Question : 12
The area of a circular play ground is ${3168}/{7}m^2$ . The diameter of the ground is
a) 22 m
b) 12 m
c) 24 m
d) 6 m
Answer »Answer: (b)
Area = $πr^2=3168/7$
$r^2 = {3168}/7×7/{22}$=144
$r =√144$ = 12m
Diameter = 24 m
Question : 13
You have a rectangular frame that is 40 cm by 60 cm. Can you put a square picture that has an area of 800 $cm^2$ completely inside the frame?
a) No
b) Yes
c) Can't say
d) Data insufficient
Answer »Answer: (b)
Question : 14
The three numbers are in the ratio 2 : 3 : 4. The sum of their cubes is 33957. The numbers are,
a) 4, 6, 8
b) 6, 9, 12
c) 12, 18, 24
d) 14, 21, 28
Answer »Answer: (d)
Let the ratio of numbers be x.
∴ numbers are 2x, 3x & 4x.
∴$(2x)^3+(3x)^3+(4x)^3$=33957
⇒$8x^3+27x^3+64x^3$=33957
⇒$99x^3$=33957
⇒$x^3=33957/99$
⇒$x^3$=343⇒x=7
∴ Numbers are 2×7,3×7,4×7
i.e. 14, 21, 28
Question : 15
$(74 × √676)- (42 × √{?})$ = 496
a) 1296
b) 1024
c) 1156
d) 1089
e) None of these
Answer »Answer: (c)
(74 × $√{676}) - 42 × √{?} = 496$
$√{?} =(74 × 26 - 496)/42 = 1428 ÷ 42 = 34= (34)^2$ = 1156
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