Mallapragada's Mathematics - (Square roots and cube roots)

Om Sri Ram          Om Sri Ram           Om Sri Ram
                                                   

(Square roots and cube roots)

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 =   =(5/4)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
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
	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