Simplification and Approximate value
### BODMAS – ( bracket of division multiplication addition and subtraction)

Step 1 – First of all solve brackets

Step 2 – After that solve powers and surds ( squares , cubes , square root , cube root etc.)

Step 3 – After that solve multiply or divide from left to right which comes first .

Step 4 – Finally solve addition or subtraction from left to right which comes first.

### Laws of integral exponents

1. = ……………. (x times)

2. =

3. =

4. =

5. =

6. =

7.

Example (7) = = 64

= = 256
64 256

8. =

**Short tricks to find square roots**

First remember the squares from 1 to 9

= 1

= 4
= 9

= 16

= 25

= 36

= 49

= 64

= 81

1. = ?

First check the unit place of this number (which is 9)

3^2 = 9

And 7^2 = 49

The unit place of the number is 3 or 7

Ignore the last two digits (09)

Remaining digits = 28

Now 28 is in between 5^2 and 6^2 ( take the smaller one i.e. 5 for the square root except unit place which is 3 or 7 )

5*6 = 30 > 28

Since 28 is small than 30 so we take smaller one in 3 and 7

= 53

2. = ?

57 and 76

4^2 = 16 and 6^2 = 36

7^2 < 57 < 8^2

7*8 = 56 < 57

Since 57 is greater than 56, so we take larger in 4 and 6

= 76

3. = ?

125 and 44

2^2 = 4 and 8^2 = 64

125 lies between the squares of 11 and 12 (smaller one is 11)

11*12 = 132 > 125

Since 125 is smaller than 132, so we take smaller in 2 and 8

= 112

**Short tricks to find cube roots**

First remember the cubes from 1 to 9

= 1
= 8

= 27

= 64

= 125

= 216

= 343

= 512

= 729

1.

First check the unit place of the given number (which is 4)

Now find from the above cubes that which cubes has unit place 4 (which is 4)

So unit digit of our cube root is 4

Now ignore the last three digits 744

Remaining digits = 2

Now 1^3< 2 < 2^3 ( take smaller one which is 1)

So our cube root is 14

2.

Unit place of this number = 6

So unit place of our cube root is 6 (6^3= 216)

Ignore the last three digits

Remaining digits = 17

2^3< 17 < 3^3 ( take smaller one which is 2 )

So our cube root is 26

3.

Unit place of this number = 8

So unit place of our cube root is 2 (2^3= 8)

Ignore the last three digits

Remaining digits = 778

9^3< 778 < 10^3 ( take smaller one i.e. 9)

Our cube root is 92

## Few questions of simplification and approximate value

1. What come in place of ?

a) 3 b) 2 c) -3 d) -2

Answer – d) -2

Solution =

=

=

= 3 – 5 = -2

2. is equal to

a) 10 b) 11 c) 21 d) 9

Answer – b) 11

Solution

= = 11

3. ………………… is equal to

a) 8 b) -7 c) 6 d) -14

Answer – a) 8

Solution : Let x = …………………….

squaring both sides

= 56 + ……………………….
= 56 + x
– x – 56 = 0
(x – 8) (x + 7) = 0

x = 8 or x = -7

hence x = 8 ( This is because square root only gives positive value )

4. simplify

a) 6/43 b) 13/54263 c) 1/43 d) 42/43

Answer – a) 6/43

Solution

= [ ]

= [ ]

=

=

=

= 6/43

5. Find the value of ……………..

a) 3.5 b) – 3.5 c) 0 d) 1

Answer – b) – 3.5

Solution Let x =
= -3.5
= – 3.5 x

x = – 3.5

6. Simplify

a) 234/17 b) 451 / 123 c) 546/119 d) 335/133

Answer – d) 335/133

Solution

=

=

=

=

=

7. If = A + C, then A + B + C is equal to

a) 2/11 b) 2/3 c) 4/11 d) 1/6

Answer – b) 2/3

solution =

=

=

=

A = 1/3 , B = 0 and C = 1/3

A + B + C = 1/3 + 1/3 = 2/3

8. is equal to

a) 13 b) 2197 c) 169 d) 1

Answer – c) 169

Solution =

= = 169

9. is equal to

a) 1 b) 2 c) 3 d) 4

Answer – c) 3

Solution = 453

= 151
= 453/151 = 3

## Problems for Practice

**Directions (1-10): What value will come in place of the question mark (?) in each of the following equation ?**

**1. **
a) 404

b) 408

c) 410

d) 414

e) 416

**2. {2.002 + 7.9(2.8 – 1.4)} = ?**

a) 11.312

b) 12.204

c)13.062

d) 14.442

e)11.006

**3.**

a) 25

b) 100

c) 150

d) 50

e) none of these

**4.** ** = ?**

a) 2.3

b) 3.4

c) 5.7

d) 8.0

e) 1

**5. = ?**

a) 140

b) 128

c) 132

d) 136

e) 144

**6.** ** ****= ?**

a) 3.45

b) 3.55

c) 3.65

d) 3.75

e) 3.85

**7. **

a) 25

b)
c) 625

d) 15

e) 5

**8. **

a) 7

b) 19

c) 18

d) 9

e) none of these

**9. **

a) 484

b) 529

c) 576

d) 625

e) 676

**10. = ?**

a) 63.5

b) 64.5

c) 65.5

d) 66.5

e) 67.5

**Directions (11-20): What approximate value will come in place of the question mark (?) in each of the following equation ?**

**11. **185% of 1359 + 18.5% of 1319 = ?

a) 2510

b) 2630

c) 2760

d) 2890

e) 3025

**12. **

a) 1625

b) 1705

c) 1775

d) 1815

e) 1855

**13. **

a) 120

b) 130

c) 140

d) 150

e) 160

**14. = ?**

a) 11

b) 15

c) 20

d) 24

e) 27

**15. + 169% of 784 = ?**

a) 2520

b) 2610

c) 2750

d) 2870

e) 2930

**16. = ?**

a) 685

b) 705

c) 815

e) 745

e) 635

**17.** ** = ?**

a) 2080

b) 2120

c) 2150

d) 2175

e) 2250

**18.** ** = ?**

a) 600

b) 650

c) 700

d) 630

e) 750

**19. = ?**

a) 550

b) 590

c) 620

d) 650

e) 690

**20.** ** = ?**

a) 50

b) 60

c) 70

d)80

e) 90

**Directions (1-10): What value will come in place of the question mark (?) in each of the following equation ?**

**21.**
a) 1

b) 2

c) 3

d) 4

e) 5

**22.**
a) 3

b) 4

c) 5

d) 6

e) 7

**23**. of of of 3080 = ?

a) 3864

b) 3948

c) 4014

d) 4124

e) none of these

**24. ** = ?

a) 14

b) 196

c) 2744

d) 38416

e) none of these

**25. ** = ?

a) 10

b) 11

c) 12

d) 9

e) 13

**Directions (26-30): What approximate value will come in place of the question mark (?) in each of the following equation ?**

**26.** = ?

a) 18

b) 20

c) 16

d) 22

e) 24

**27.** 48.5% of 7842 + ? % of 1318 = 4515

a) 42

b) 48

c) 54

d) 57

e) 60

**28. ** = ?

a) 59

b) 61

c) 63

d) 65

e) 67

**29.** = ?

a) 1200

b) 1250

c) 1300

d) 1350

e) 1400

**30.** = ?

a) 700

b) 720

c) 740

d) 760

e) 780

**Answers**

1. d 2. c 3. d 4. d 5. c

6. c 7. e 8. a 9. c 10. e

11. c 12. a 13. d 14. b 15. e

16. d 17. a 18. d 19. e 20. c

21. d 22. c 23. a 24. a 25. b

26. a 27. c 28. b 29. c 30. b

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