Squares, roots and powers
Squares, roots and powers

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Squares, roots and powers

1.4.1 Try some yourself

Activity 8

If a litre is one cubic decimetre, how many litres are there in a cubic metre?

Answer

Since a litre is one cubic decimeter, the question is asking how may cubic decimetres are in a cubic metre.

1 metre = 10 decimetres

so 1 m3 = 103 cubic decimetres.

Hence there are 1000 litres in a cubic metre.

Activity 9

Find the following without using your calculator, as an estimate for the calculator work in the next question.

  • (a) (1)3

  • (b) 33

  • (c) 1003

  • (d) 0.13

Answer

  • (a) (1)3 = 1 × 1 × 1 = 1 × 1 = 1

  • (b) 33 = 3 × 3 × 3 = 9 × 3 = 27

  • (c) 1003 = 100 × 100 × 100 = 10 000 × 100 = 1000 000 (a million)

  • (d)

Activity 10

Use your calculator to find the following.

  • (a) (1.2)3

  • (b) 3.33

  • (c) 1013

  • (d) 0.1213

Answer

  • (a) Estimate: (1)3 = 1.

    Calculate: (1.2)3 = 1.728.

  • (b) Estimate: 33 = 27.

    Calculate: 3.33 = 35.937.

  • (c) Estimate: 1003 = 1000 000.

    Calculate: 1013 = 1030 301.

  • (d) Estimate: .13 = .001.

    Calculate: 0.1213 = 0.00177 (3 s.f.)

Activity 11

What are the following?

  • (a)

  • (b)

Answer

  • (a) = 1 since 13 = 1.

  • (b) = 10 since 103 = 1000.

Activity 12

Find the volume of a one-foot cube in cubic metres (1 foot = 30.48 cm). Estimate your answer first. Round your answer to three decimal places.

Answer

To estimate an answer, choose a simple approximation, say

1 foot 30 cm = 0.3 m.

Then 1 foot cubed (0.3)3 = 0.027 m3.

More accurately, 1 foot = 30.48 cm = 0.3048 m.

So 1 foot cubed = (0.3048)3 = 0.028 m3 to three d.p.

Activity 13

Without using your calculator, find the following, as estimates for the calculator work in Question 7.

  • (a) 92

  • (b) 43

  • (c)

  • (d)

  • (e) (3)2

Answer

  • (a) 92 = 9 × 9 = 81

  • (b) 43 = 4 × 4 × 4 = 16 × 4 = 64

  • (c) = 8 (since 82 = 64)

  • (d)

  • (e) (3)2 = 3 × 3 = 9

Activity 14

Use your calculator to find:

  • (a) 9.422

  • (b) 3.653

  • (c)

  • (d) 0.333

  • (e) (2.713)2

Use your answers to the previous question as rough checks. Round your answers to four decimal places.

Answer

  • (a) 9.422 = 88.7364

  • (b) 3.653 48.6271

  • (c) 8.3666

  • (d) 0.333 0.0359 (check this by calculating , the estimate from 3(d) above, as a decimal.

  • (e) (2.713)2 7.3604 (N.B. To get this answer on a calculator, remember the brackets.)

MU120_4M4

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