Roots, Powers and Exact Values - Worksheets, Questions and Revision

18 original exam-style questions - 4 pages of questions with a full mark scheme - free printable PDF.

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KS3 · Number

KS3.M-N15 Roots, Powers and Exact Values

AQA KS3.M-N15 · Calculators not allowed · about 60 minutes
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Evaluate each exact root value.
(a)√81(1)
(b)cube root of 27(1)
(c)√49(1)
2
Find each exact power.
(a)72(1)
(b)43(1)
3
Simplify the surd √50 and give the answer in simplest exact form.
(2)
4
Simplify √72 giving the exact form a √b with b simplified.
(2)
5
Simplify √18 and give your answer in simplest exact form.
(2)
6
Simplify √8 in exact form.
(2)
7
Write √45 in the form a √b with b simplified.
(2)
8
Give the exact values.
(a)(√3)2(1)
(b)√5 x √5(1)
9
Find each cube root exactly.
(a)cube root of 64(1)
(b)cube root of 216(1)
10
Evaluate the powers exactly.
(a)25(1)
(b)53(1)
11
Work out √2 x √8 and give the answer in exact form.
(2)
12
Multiply the surds and simplify: √3 x √12.
(2)
13
Simplify and combine: √20 + √5. Give the exact form.
(2)
14
Give the positive square root of 49.
(1)
15
Without using a calculator, state whether √50 is greater than, equal to or less than 7. Give a brief reason.
(1)
16
Simplify (√5)3 and give the exact form.
(2)
17
A square garden has area 50 m2. Find the exact length of one side in simplest surd form.
(2)
18
Stretch: Express √12 + √27 in the form k √3. Find k and show the steps.
(2)
Mark scheme · KS3.M-N15 Roots, Powers and Exact Values

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18