10, ఏప్రిల్ 2015, శుక్రవారం

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