Estimating a root to the nearest tenth can be done a number of ways. The method shown here is to identify the tenths whose squares bracket the value of interest.

You have answered the questions of parts 1 to 3.

You are given that ...

7.2² = 51.84

7.3² = 53.29

This means 53 lies between 7.2² and 7.3², so √53 lies between 7.2 and 7.3.

53 is closer to 7.3², so √53 will be closer to 7.3 than to 7.2.

7.3 is a good estimate of √53 to the tenths place.

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<em>Additional comment</em>

For an integer n that is the sum of a perfect square (s²) and a remainder (r), the square root is between ...

s +r/(2s+1) < √n < s +r/(2s)

For n = 53 = 7² +4, this means ...

7 +4/15 < √53 < 7 +4/14

7.267 < √53 < 7.286

Either way, √53 ≈ 7.3.

The root is actually equal to the continued fraction ...

$\sqrt{n}=\sqrt{s^2+r}=s+\cfrac{r}{2s+\cfrac{r}{2s+\dots}}$

7 0

1 year ago

Answer asap

Lana71 [14]

Two figure in front

h=16+17 = 33 m
l=18 m
width = 13 m
Volume = lwh = 18*13*33 =7722 m^2

Two figures at the back

h=16 m
l=18+18 =36 m
width = 15 m

Volume = lwh =36*15*16 =8640 m^2

Total volume = 7722+8640 = 16362 m^2

5 0

2 years ago