8.Mallapragada's. Mathematics (Square roots and cube roots)

 (Square roots and cube roots)

Sl. No.	/Problems	Answers
1.	Evaluate  root of 6084 by fraction method
2.	Find the square root of  1471369
3.	Evaluate  :root 248 +root 51 +root 169=
4.	What is the square root of 0.0009?
5.	Fiend the value of root 1 to the power of 9/16
6.	Find the value of 3 up to three places of decimal
7.	root 176 + root 2401=?
8.	Square  root ate of 225/729 – Square rout  of 25/144 + square rout of 16/81 ?
9	Square Root of  (a+2)(b+3)/c + 1 if a=6 b=15, c= 3 find the value?
10	(86.49)1/2 + {(5+x)2}1/2 = 12.3  find x
11	X + y+root xy   If x = 6, y= 24 find ?
12	If y= 10 then what is the value of 10y  root y3 – y2 = ?
13	52/x =     (169/289)1/2find x
14	(x/15)(x/135) = 1
15	9/2/x = x/32 find x value
16	0.15  x2 =15
17	(3x)1/2 = 729 find the value of x
18	(x/169)1/2 = 54/39
19	root of 14x18 x X=84
20	(0.0169 x X)1/2 =1.3
21	What is the smallest number by which 3600 be divided to make it a perfect cube?
22	By what least number 675 be multiplied to obtain a number which is a perfect cube?
23	The largest four-digit number which is a perfect cube is
24	The cube root of .000216 is
25	A = 51/2+1/51/2-1    B= 51/2-1/51/2+1 The value of a2 +ab+b2/ a2 -ab+b2
26	X= {7-4 (3)1/2} Then the value of (x + 1/x)
27	Root 2 = 1.414 the square root of root 2  -1/root 2 +1 is nearest to
28	Root 50 x root 98 is equal to?
29	The square root of (7 + 3 root 5) (7 - 3 root 5)
30	The value of root 0.16/0.4 =?

                                         

Answers of above problems

1.	Root of 6084   2)6084, 2)3042, 3)1521,                            3)507, 13)169, 13               6084= 22 x 32 x132 = 2 x 3 x 13= 78  Find the square root of  1471369 1 1471369 1213 1 22   47   44 241     313     241 2423       7269       7269 Ans 1213.
3.	Evaluate :root 248 + root 51 +root 169      248 + 51 + 13 =248 + root 64
4.	0.0009= 9/10000 = 32/1002 =(3/100)2=.03
5.	1 9/16 =   =(3/4)2
6.	=1.732 1 3.000000 1.732 1 27   200   189 343     1100     1029 3462       7100       6924
7.	root 176 +root 2401 (176)1/2 + (2401)1/2 = (176)1/2  +{(49)2}1/2= (225)1/2            Ans. 15
8.	Square root of 225/729 – Square rout  of 25/144 +      square rout of 16/81 ?      Ans. 152/272  - 52 /122 + 42+ /92 = 15/27 + 5/12 – 4/9 =              LCM of 27,12,9= 3)9,4,3, 3)3,4,1 = 3x3x3x4=108                  (60 + 45 -48 )/108 = 57/108
9	(a+2)(b+3)/c + 1 if a=6 b=15, c= 3 find the value? Ans. {6+2)(15+3)/(3+1)}1/2 = {8 x 18/4}1/2              {144/4}1/2  = {{12/2}2}1/2  = Ans. 6
10	(86.49)1/2 + {(5+x)2}1/2 = 12.3  find x Find the square root of   9 86.49 9.3 81 183   5.49   5.49     0 Ans 9.3 9.3+{(5+x)2}1/2=12.3 9.3+5+x=12.3 X=12.3-14.3=-2
11	x+y+root  xy If x = 6, y= 24 find ? 6+24 (6x24)1/2  = 30+ (144)1/2= 0+12=42
12	If y= 10 then what is the value of 10y root of         y3 – y2 = ? Ans. 10x10 (103-102)1/2 = 100(1000-100) ½               100 ( 900) ½  = 100 x (302) ½ = 3000
13	52/x =   root (169/289) find x 52/x= {132/172}1/2 = {(13/17)2}1/2 13x = 17 x 52  = x = (17 x 52)/13 =68
14	(x/15)(x/135) = 1 Ans. x2 =15 x 135 =2025  5x405,5x5x81,5x5x9x9          x2  = 452 x= 45
15	9/2/x = x/32 find x value X2 = 9/2 x 32 =9x16 = 144= 122  x=12
16	0.15  x2 =15, 15/100 x 1/x2=15 X2 = 15 x 100/15 = 102 = x=10
17	(3x)1/2 = 729 find the value of x Ans. (3x)1/2 = 35 , x/2 = 5, x=10
18	(x/169)1/2 = 54/39 Ans. x 1/2/13 =54/39  X1/2 = (54 x 13)/39 = 18= x= 182
19	Root of  14x18 x X=84, Squaring in both side Ans. 14 x 18 x X = 84 x84          X = (84x84)/14x18 = 6x84/18 = 2x84/6          X = 28
20	(0.0169 x X)1/2 =1.3 squaring in both side 0.0169 x X = 1.3 x 1.3    X = 1.69/0.0169 = 100
21	What is the smallest number by which 3600 be divided to make it a perfect cube? 3600= 23 x 52 x 32 x 2 = To make it perfect cube, it must be devidded by 52 x 32 x 2 = i.e450
22	By what least number 675 be multiplied to obtain a number which is a perfect cube? 675= 5x5x3x3x3 = 52 x33 = To make perfect cube multiply by 5
23	The largest four-digit number which is a perfect cube is Ans. 9261 is a perfect cube satisfying the given property
24	The cube root of .000216 is (.000216)1/3 = {216/106}1/3  = (63) 1/3/ {106}1/3 6/102 = 6/100 0.06
25	A = 51/2+1/51/2-1    B= 51/2-1/51/2+1 The value of a2 +ab+b2/ a2 -ab+b2+ Ans.  A = {51/2+1/51/2-1}  51/2+1/51/2+1 =(51/2+1)2/5-1            = 5 +251/2 +1/4,  6 + 2(51/2)/4 =3+51/2/2       B= {51/2-1/51/2+1}{51/2-1/51/2-1}={51/2-1}2/4              3-51/2/2 A2 + B2 =  {3+51/2}2/4  - {3-51/2}2/4 = 2(9+5)/4 =7
26	X= {7-4 (3)1/2} Then the value of (x + 1/x)   {7-4 (3)1/2} + 1/{7-4 (3)1/2} x {7+4 (3)1/2}                                                                    /{7+4 (3)1/2}= {7-4 (3)1/2} + {7+4 (3)1/2}/ 72 - 42 3=14/49-48 =14
27	Root 2 = 1.414 the square root of root 2  -1/root 2 +1 is nearest to Ans. (21/2 -1) (21/2 -1)          ---------------------    = (21/2 -1)2/2-1             (21/2 +1) (21/2 -1)           =1.414-1=.414
28	Root 50 x root 98 is equal to? Ans. root 50 x 98 = (4900)1/2 = {(70)2}1/2 = 70
29	The square root of (7 + 3 root 5) (7 - 3 root 5) Ans. 72 – {3 (5)1/2}2 = 49 – 9 x 5= 4 22 = Ans. 2
30	The value of root 0.16/0.4 =?
	Ans. {.16/.40}1/2 = (16/40) ½ = (4/10) ½ = (0.4) ½=            0.63