# Algebra: Substitution with Squares and Square Roots (2)

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

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Substitute Numerical Values for Formulae/Expressions

Difficulty level:

### 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

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

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

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

-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

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

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

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

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

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

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

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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