Simplify the following surds :
1) 2√21 × √27 ÷ √343
2) 7√5 × √125 ÷ 2√27

1)

2)

Step-by-step explanation:

* Lets explain how to simplify a square root

1)

∵ × ÷

∵ ×

∴ = ×

∵ = × ×

∵ × = 3

∴ =

∴ × =

  × ×

∵ × = 3

∵ 2 × 3 × 3 = 18

∴ × =

∵ = × ×

∵ × = 7

∴ =

∵ × ÷ =

  ÷

∵ ÷ = 1

∴ × ÷ =

2)

∵ × ÷  

∵ = × ×

∵ × = 5

∴ =

∴ × =

  ×

∵ × = 5

∴ × = 7 × 5 × 5 = 175

∵ = × ×

∵ × = 3

∴ =

∴ × ÷ =

  175 ÷ =

∵ not in the simplest form because

  the denominator has square root

∴ Multiply up and down by

∴   =

∴   =

∴ × ÷ =

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.

from the figure we get,

the x axis shows   the months and,

the y-axis shows the number of satisfied customer.

each line or each cell in upward direction (y-axis) shows 500.

the appropriate scale for the y - axis is: -

a = 2000 customers

b = 4000 customers

c = 6000 customers

d = 8000 customers

e = 10000 customers

f = 12000 customers

g = 14000 customers