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mathematics UK Year 9 Mathematics (KS3)
 
Solved problems for the chapter:
 

Square root and cube root

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View the theory »
Indices with rational exponents
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↓   Show theory [1]   ↓


Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:square_root_and_cube_root/4146/


Example 1.
Calculate the numerical expression by first writing it as powers with rational exponents.

    
Example 2.
Calculate the numerical expression by first writing it as powers with rational exponents.

    
3.

Arrange in descending order:











    
4.

Calculate:









    
5.

Evaluate the square roots:









    
6.

Calculate:







    
7.

Evaluate the following:









    
8.
Write down the powers with rational exponents and calculate.

    

9.
Calculate:

    
10.

Calculate the value of

   
11.
Calculate:

    
12.
Calculate:

    
13.
Rounding the result to three significant figures, use a calculator to solve:

    
14.
Calculate:

    
15.
Rounding the result to three significant figures, use a calculator to solve:

    
16.

Calculate with a pocket calculator and round the result to four significant figures.

    
17.
Rounding the result to three significant figures, use a calculator to solve:

    
18.

Calculate with a calculator and round the result to four significant figures.

    

19.

Calculate with a calculator and leave the result in three significant figures.

    
20.

Calculate with a calculator and leave the result in three decimal places.

    
21.

Calculate with a calculator and leave the result to three decimal places.

    
22.

Calculate:


.

    
23.

Calculate:


    
24.
Calculate:

    
25.

Calculate:


    
26.

Calculate:

   
27.

Calculate:


    
28.

Calculate with a calculator and leave the result in two significant figures.

    

29.

Check if the equation below is correct:


    
30.

Check if the equation below is correct:


    
31.

Check if the equation below is correct:


    
32.
Calculate:

    
33.

Check if the equation below is correct:


    
34.

Simplify

   
35.

Simplify

   
36.

Simplify

   
37.

Evaluate:


    
38.

Simplify .

    

39.

Simplify

   
40.
Write down the powers with rational exponents and calculate.

    
41.
Calculate the numerical expression by first writing it as powers with rational exponents.

    
42.
Using a pocket calculator, calculate the next root and round the result to three places exactly.

    
43.

Calculate and arrange in descending order:









    
44.

Arrange the numbers in descending order:











    
45.

Calculate:


    
46.

Calculate the following:





    
47.

Calculate:







    
48.

Evaluate the following:









    

49.
Using a pocket calculator, calculate the next root and round the result to three places exactly.

    
50.
Using a pocket calculator, calculate the next root and round the result to three places exactly.

    
51.
Using a pocket calculator, calculate the next root and round the result to three places exactly.

    
52.
Calculate the numerical expression by first writing it as powers with rational exponents.

    
53.

Calculate:


    
54.

Calculate the square roots:







    
55.

Write down the square root of the number and use a pocket calculator to calculate it to four significant figures.

    
56.
Write down the powers with rational exponents and calculate.

    
57.

Without using a calculator, evaluate:


    
58.

Without using a calculator, evaluate:


    

59.

Without using a calculator, calculate:


    
60.

Using a pocket calculator, calculate and round to two decimal places:


    
61.

Using a pocket calculator, calculate and round to four significant places:


    
62.

Simplify without a calculator.

    
63.

Using a pocket calculator, calculate and round to four significant figures:


    
64.

Simplify without using a calculator.

    
65.

Using a pocket calculator, calculate and round to four decimal places:


    
66.

Simplify

   
67.

Simplify without using a calculator.

    
68.

Simply:


    

69.

Simply:


    
70.

Simply:


    
71.

Simplify:


    
72.

Simply:


    
73.

Simply:


    
74.

Evaluate:


    
75.
Rationalize

    
76.

Determine the additive inverse of the numbers below: