# Apply Fractional Indices

In this worksheet, students will revise and apply fractional indices.

Key stage:  KS 3

Curriculum topic:   Number

Curriculum subtopic:   Understand Integer Powers/Real Roots

Difficulty level:

### QUESTION 1 of 10

A fractional index of a half is the equivalent of finding a square root.

Using the rules for multiplying powers, notice that:

9½ x 9½ = 91

Which is then the equivalent of:

√9 x √9 = 9

Therefore,

9½ = √9 = 3

Using this explanation, let's apply the same method to some questions.

Select the answer which is equal to:

16½

8

16½

4

Select the answer which is equal to:

36½

6

36½

18

Select the answer which is equal to:

1½

1

½

1.5

Select the answer which is equal to:

10½

5

√10

10.5

Select the answer which is equal to:

25½

25½

√12.5

√25

Select the answer which is equal to:

100½

10½

50

10

Type the answer which is equal to:

0½

Type the answer which is equal to:

10000½

Select the answer which is equal to:

1000½

√1000

100

33.3

Type the answer which is equal to:

16900½

• Question 1

Select the answer which is equal to:

16½

4
EDDIE SAYS
16½ x 16½ = 16¹ √16 x √16 = 16 Therefore, 16½ = √16 = 4 How are you getting on?
• Question 2

Select the answer which is equal to:

36½

6
EDDIE SAYS
36½ x 36½ = 36¹ √36 x √36 = 36 Therefore, 36½ = √36 = 6
• Question 3

Select the answer which is equal to:

1½

1
EDDIE SAYS
1½ x 1½ = 1¹ √1 x √1 = 1 Therefore, 1½ = √1 = 1 Did you find this question difficult or easier?
• Question 4

Select the answer which is equal to:

10½

√10
EDDIE SAYS
10½ x 10½ = 10¹ √10 x √10 = 10 Therefore, 10½ = √10
• Question 5

Select the answer which is equal to:

25½

√25
EDDIE SAYS
25½ x 25½ = 25¹ √25 x √25 = 25 Therefore, 25½ = √25 You're making fantastic progress! You're now halfway through.
• Question 6

Select the answer which is equal to:

100½

10
EDDIE SAYS
100½ x 100½ = 100¹ √100 x √100 = 100 Therefore, 100½ = √100 = 10
• Question 7

Type the answer which is equal to:

0½

0
EDDIE SAYS
0½ x 0½ = 0¹ √0 x √0 = 0 Therefore, 0½ = √0 = 0 Hopefully you identified that zero to the power of any value is always zero.
• Question 8

Type the answer which is equal to:

10000½

100
EDDIE SAYS
10000½ x 10000½ = 10000¹ √10000 x √10000 = 10000 Therefore, 10000½ = √10000 = 100 Did you read the question carefully? It's easy to make mistakes in your calculations when working with larger values so stay vigilant!
• Question 9

Select the answer which is equal to:

1000½

√1000
EDDIE SAYS
1000½ x 1000½ = 1000¹ √1000 x √1000 = 1000 Therefore, 1000½ = √1000 One more question to go, then you can take a break.
• Question 10

Type the answer which is equal to:

16900½

130
EDDIE SAYS
16900½ x 16900½ = 16900¹ √16900 x √16900 = 16900 Therefore, 16900½ = √16900 = 130 Great focus! That's another activity ticked off.
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