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Algebra: Substitution with Squares and Square Roots (2)

In this worksheet, students substitute numbers into expressions containing squares and square roots.

'Algebra: Substitution with Squares and Square Roots (2)' worksheet

Key stage:  KS 3

Curriculum topic:  Algebra

Curriculum subtopic:  Substitute Numerical Values for Formulae/Expressions

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

When we substitute a number for a letter, we simply replace the letter with the number.

However, we must remember that 4b means 4 × b and 4b2 means 4 × b × b.

 

Example

Work out the value of the following expression when a = 4 and b = 9

3a2 - 7 - 2√b

 

Answer

3a2 - 7 - 2b

 = (3 × a2) - 7 - (2 × b)

= (3 × 42) - 7 - (2 x √9)

= (3 × 16) - 7 - (2 x 3)

= 48 - 7 - 6

= 35 

Work out the value of the following expression when a = 4 and b = 2

3a2  + b2

 

Work out the value of the following expression when a = 4 and b = 2

3√a  + b2

 

Work out the value of the following expression when a = 4 and b = 2

3√a  - 2b2

 

Work out the value of the following expression when a = 9 and b = 1

4√a  - 6b2

Work out the value of the following expression when a = 9 and b = 1

4√a  + 5b2

Work out the value of the following expression when a = 2 and b = 1

4a2  + 5√b

 

Work out the value of the following expression when a = 3 and b = 0

4a2  + 5√b

Work out the value of the following expression when a = -3 and b = 0

3a2  - 3√b

Work out the value of the following expression when a = 3 and b = 25

3a2  - 3√b

Work out the value of the following expression when a = -2 and b = 64

4a2  - 2√b

  • Question 1

Work out the value of the following expression when a = 4 and b = 2

3a2  + b2

 

CORRECT ANSWER
52
EDDIE SAYS

Substitute in the values

3 x 42 + 22

Evaluate Indices first

3 x 16 + 4

Apply BODMAS

48 + 4

52

  • Question 2

Work out the value of the following expression when a = 4 and b = 2

3√a  + b2

 

CORRECT ANSWER
10
EDDIE SAYS

Substitute in the values

3 x √4 + 22

Evaluate Indices and roots first

3 x 2 + 4

Apply BODMAS

6 + 4

10

  • Question 3

Work out the value of the following expression when a = 4 and b = 2

3√a  - 2b2

 

CORRECT ANSWER
-2
EDDIE SAYS

Substitute in the values

3 x √4 - 2 x 22

Evaluate Indices and roots first

3 x 2 - 2 x 4 

Apply BODMAS

6 - 8

-2

  • Question 4

Work out the value of the following expression when a = 9 and b = 1

4√a  - 6b2

CORRECT ANSWER
6
EDDIE SAYS

Substitute in the values

4 x √9 - 6 x 12

Evaluate Indices and roots first

4 x 3 - 6 x 1 

Apply BODMAS

12 - 6

6

  • Question 5

Work out the value of the following expression when a = 9 and b = 1

4√a  + 5b2

CORRECT ANSWER
17
EDDIE SAYS

Substitute in the values

4 x √9 + 5 x 12

Evaluate Indices and roots first

4 x 3 + 5 x 1 

Apply BODMAS

12 + 5

17

  • Question 6

Work out the value of the following expression when a = 2 and b = 1

4a2  + 5√b

 

CORRECT ANSWER
21
EDDIE SAYS

Substitute in the values

4 x 2+ 5 x √1

Evaluate Indices and roots first

4 x 4 + 5 x 1 

Apply BODMAS

16 + 5

21

  • Question 7

Work out the value of the following expression when a = 3 and b = 0

4a2  + 5√b

CORRECT ANSWER
36
EDDIE SAYS

Substitute in the values

4 x 3+ 5 x √0

Evaluate Indices and roots first

4 x 9 + 5 x 0 

Apply BODMAS

36 + 0

36

  • Question 8

Work out the value of the following expression when a = -3 and b = 0

3a2  - 3√b

CORRECT ANSWER
27
EDDIE SAYS

Substitute in the values

3 x (-3)- 3 x √0

Evaluate Indices and roots first

3 x 9 - 3 x 0 

Apply BODMAS

27 - 0

27

  • Question 9

Work out the value of the following expression when a = 3 and b = 25

3a2  - 3√b

CORRECT ANSWER
12
EDDIE SAYS

Substitute in the values

3 x 3- 3 x √25

Evaluate Indices and roots first

3 x 9 - 3 x 5 

Apply BODMAS

27 - 15

12

  • Question 10

Work out the value of the following expression when a = -2 and b = 64

4a2  - 2√b

CORRECT ANSWER
0
EDDIE SAYS

Substitute in the values

4 x (-2)- 2 x √64

Evaluate Indices and roots first

4 x 4 - 2 x 8 

Apply BODMAS

16 - 16

0

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