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Flashcards in Summer 9 Deck (37):
1

Is √16 a surd?

No because √16 = 4 (a whole number).

2

Simplify √12

√12 = √4*3 = √4 * √3
= 2√3

3

5º =

1

4

6² * 6³ =

² + ³ = ⁵
6⁵

5

6³ / 6² =

³ - ² = ¹

6

Write 235,000,000 in standard form.

2.35 * 10⁸

7

Write 1.9 * 10⁹ as an ordinary number.

1,900,000,000

8

5.2 * 10³ * 4.1 * 10⁹ =

5.2 * 4.1 = 21.32
³ + ⁹ = ¹² (10¹²)
21.32 * 10¹² → 2.132 * 10¹³

9

6.5 * 10⁶ / 5 * 10³ =

6.5 / 5 = 1.3
⁶ - ³ = ³ (10³)
1.3 * 10³

10

What must you remember when doing standard form?

A * 10ⁿ where 1 ≤ A < 10

11

5¹ =

5

12

Draw the table for angles and sine, cosine and tangent.

Is all the table correct?

13

x½ =

²√x

14

What does O, H and A stand for?

O: opposite
H: hypotenuse
A: adjacent

15

What are the trigonometry triangles?

/ O \
/ S | H \
______

/ A \
/ C | H \
______

/ O \
/ T | A \
______

16

√3 * √3 =

3

17

(√3)² =

3

18

4√2 + 3√2 + 2√2 = ?

4 + 3 + 2 = 9
4√2 + 3√2 + 2√2 = 9√2

19

√48 ÷ √12 =

√48 / 12
= √4
= 2

20

x⅓ =

³√x

21

81^-½ =

1/81^½
= 1/√81
= 1/9

22

a-ⁿ =

1/aⁿ

23

(5²)³ =

² * ³ = ⁶
= 5⁶

24

c * c * c * c * c / c * c =

25

Simplify √18

1) Find the largest square factor (√9) and the other factor that it needs to be multiplied by (√2):
√9 * √2 = √18
2) Simplify the square factor: √9 = 3
3) Form:
3√2

26

Simplify √40

√40 = √4 * √10
√4 = 2
√40 = 2√10

27

Simplify √200

√100 * √2 = √200
√100 = 10
√200 = 10√2

28

What is √80 + √20

√80 = √16 * √5 = 4√5
√20 = √4 * √5 = 2√5
4√5 * 2√5 = 6√5

29

Prove that:
2√3 * 4√3 ≠ 8√3

2 * 4 * √3 * √3 =
8 * (√3)² =
8 * 3 = 24

30

Prove that:
√9 * √4 ≠ √13

√9 = 3
√4 = 2
3 * 2 = 6
6 ≠ √13

31

A rectangle has a width of √8 and a length of √5. What is its area?

a = √8 * √5 = √40
√40 = √4 * √10 =
2√10

32

6 * 2√5 =

6(2√5) =
12√5

33

(3 * 10⁴) * (4 * 10⁵) =

12 * 10⁹ =
1.2 * 10¹º

34

8²/³ =

8²/³ = (³√8)²
³c8 = 2 and 2² = 4
(³√8)² = 4

35

16^-³/² =

16^-³/² = 1 / 16³/² = (²√16)³
²√16 = 4 and 4³ = 64
1 / 16³/² = 1/64

36

a^-ᵐ/ⁿ =

1 / (ⁿ√a)ᵐ

37

aᵐ/ⁿ =

(ⁿ√a)ᵐ