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Th84.64ree methods;-

  1. use the surd sign on a calculator e.g. (sqrt) / 4 = +/- 2

  2. Use a rather complex arithmetica system of long division.

  3. Use a time consuming but simpler method. e.g. sqrt(90)

To answer

We know sqrt(81) = 9

Sqrt(100) = 10

Since '90' is between 81 and 100 , then the square root is between '9' & '10'

Then by trial and error

9.1^(2) = 82.81 too small

9.2^(2) = 84.64 too small

9.3^(2) = 86.49 too small

9.4^(2) = 88.36 too small

9.5^(2) = 90.25 too big

So we need a decimal number between 9.4 & 9.5 say 9,45

9.45^(2) = 89.3025 too small

9.46^(2) = 89.4916 too small

et. seq.

The acutal value is sqrt(90) = 9.486832981....

In Surd form sqrt(90) = sqrt(10 x 9) = sqrt(10) X sqrt(9) = sqrt(10) x 3

or

3 sqrt(2) sqrt(5)

Since '2' & '5' are prime numbers, their respective square roots are Irrational Numbers.

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lenpollock

Lvl 16
1d ago

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