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### Surds and Indices

The value of (√8)1/3 is:

2

25

20

22

Solutions

If 3x-y=81 and 3x+y = 729, what is x?

4

5

8

10

Solutions

3x-y x 3x+y = 81 x 729
3x-y+x+y = 34 x 36
32x = 310
x = 5

If 5a = 3125, then the value of 5(a-3) is

25

125

625

1625

Solutions

5a = 3125 which is equal to 55
therefor a = 5
therefor 55-3 = 52
25

(256)0.16 x (256)0.09 = ?

4

16

64

256.25

Solutions

(256)0.16 x (256)0.09 = (256)0.16 - 0.09
(256)0.25
(256)25/100
(256)1/4
(44)1/4
(41)

The value of (10)150 ÷ (10)146

1000

10000

100000

106

Solutions

(10)150 ÷ (10)146
(10)150 - 146
104
10000

(0.04)-1.5

25

125

250

625

Solutions

(0.04)-1.5
(4/100)-1.5
(1/25)-(3/2)
(25)3/2
(52)3/2
(53)
125

If m and n are whole number such that mn = 121, the value of (m - 1)n+1 is

1

10

121

1000

Solutions

We know that 112 = 121
Putting m = 11 and n = 2, we get : (m-1)n+1 = (11 - 1)2+1 = 103 = 1000

(17)3.5 x (17)? = 178

2.29

2.75

4.25

4.5

Solutions

Let (17)3.5 x (17)x = 178
(17)3.5+x = 178
3.5 + x = 8
x = 4.5

If 3(x-7) = 27 and 3(x+y) = 243 then x is equal to.

0

2

4

6

Solutions

3x - y = 27 = 33    <=>    x - y = 3 ....(i)

3x + y = 243 = 35    <=>    x + y = 5 ....(ii)

On solving (i) and (ii), we get x = 4.

if $x=3+2\sqrt{2}$ , then the value of $\sqrt{x}-\frac{1}{\sqrt{x}}$ is:

1

2

$2\sqrt{2}$

$3\sqrt{3}$

Solutions

$\sqrt{x}-\frac{1}{\sqrt{x}}=x+\frac{1}{x}-2$
$3+2\sqrt{2}+\frac{1}{3+2\sqrt{2}}-2$
$3+2\sqrt{2}+\frac{1}{3+2\sqrt{2}}\ast \frac{3-2\sqrt{2}}{3-2\sqrt{2}}-2$
$\left(3+2\sqrt{2}\right)+\left(3+2\sqrt{2}\right)-2$
4

$\sqrt{8}-\sqrt{4}-\sqrt{2}$ Equal to = ?

$2-\sqrt{2}$

$\sqrt{2}-2$

2

-2

Solutions

(64)4 ÷ (8)5 = ?

88

82

812

83

If 310 x 272 = 92 x n then the value of n is = ?

10

12

15

30

I there is