SQUARE ROOT OF DECIMAL NUMBERS BY DIVISION METHOD

Simplify the square roots.

Problem 1 :

√35.88

Solution :

Step 1 :

We decompose the value that we find before the decimal as a product of two same values.

5 x 5 = 25 but 6 x 6 = 36 > 35

So, we choose 5 x 5 = 25.

Step 2 :

Do the subtraction, bring down the next two digits to the next step.

Step 3 :

Multiply the quotient by 2 and put it outside of division. 

Step 4 :

2 x 5 = 10

Near 10, we have to use one new number, multiply this value by the value that we have written at the top.

109 x 9 = 981 < 1088

Repeat step 2 .

So, the square root of 35.88 is 5.989.

Problem 2 :

√36.46

Solution :

So, the square root of 36.46 is 6.038.

Problem 3 :

√89.87

Solution :

So, the square root of 89.87 is 9.479.

Problem 4 :

√99.80

Solution :

So, the square root of 99.80 is 9.989.

Problem 5 :

√62.25

Solution :

So, the square root of 62.25 is 7.889.

Problem 6 :

√97.81

Solution :

So, the square root of 97.81 is 9.889.

Problem 7 :

A checkerboard is 8 squares long and 8 squares wide. The area of each square is 14 square centimeters. Estimate the perimeter of the checkerboard.

Solution :

Area of each small square = 14 square cm

Let x be the side length of the square.

x² = 14

x = √14

x = 3.74

Length of checkboard = 8(side length of square)

= 8(3.74)

= 29.92

Width of checker board = 8(side length of square)

= 8(3.74)

= 29.92

Perimeter of square board = 4(29.92)

= 119.68 cm

Problem 8 :

Which number is greater? Explain.

a) √20, 10

b) √15, -3.5

c) √133, 10  3/4

d) 2/3, √(16/81)

e)  -√0.25, -0.25

f) -√182, -√192

Solution :

a) √20, 10

20 is not perfect square, the nearest perfect square are 16 and 25.

4 < √20 < 5

√20 = 4.4.....

So, √20 < 10

b) √15, -3.5

15 is not perfect square, the nearest perfect square are 9 and 16.

3 < √15 < 4

√15 = 3.8....

So, √15 > - 3.8

c) √133, 10  3/4

√121 = 11

√144 = 12

11 < √133 < 12

10 3/4 = 43/4

= 10.75

√133 > 10  3/4

d) 2/3, √(16/81)

√(16/81) = √(4 x 4)/(9 x 9)

= 4/9

To compare the fractions 2/3 and 4/9, we have to convert them into like fractions.

= (2/3) x (3/3)

= 6/9

Comparing the fractions 6/9 and 4/9, 6/9 is the greater.

2/3 > √(16/81)

e)  -√0.25, -0.25

-√0.25 =  -√(0.5 x 0.5)

= -0.5

Comparing the decimals -0.5 and -0.25, we get

-√0.25 < -0.25

f) -√182, -√192

-√169 < -√182 < -√196

-13 < -√182 < -14

Approximate value of -√182 is -13.4

Approximate value of -√192 is -13.8

-√182 > -√192

Problem 9 :

The area of a four square court is 66 square feet. Estimate the length s of one of the sides of the court

Solution :

Area of square court = 66 square feet

Side length of square is s.

s² = 66

s = √66

Side length of the square is 8.12 feet.

Problem 10 :

The maximum distance (in nautical miles) that a radio transmitter signal can be sent is represented by the expression 1.23 √h , where h is the height (in feet) above the transmitter.

Estimate the maximum distance x (in nautical miles) between the plane that is receiving the signal and the transmitter. Round your answer to the nearest tenth

Solution :

= 1.23 √h

Applying the value of h, we get

= 1.23 √22000

= 1.23(148.32)

= 182.43

Problem 11 :

The velocity v (in meters per second) of a roller coaster is represented by the equation v = 3 √6r, where r is the radius of the loop. Estimate the velocity of a car going around the loop. Round your answer to the nearest tenth.

Solution :

v = 3 √6r

Here r = 16.764 m

Applying the value of r, we get

v = 3 √6(16.764)

= 3√100.58

= 3(10)

= 30

Approximately the velocity is 30 m.

Problem 12 :

Is √(1/4) a rational number? Is √(3/16) a rational number ? Explain.

Solution :

√(1/4) = √(1 x 1)/(2 x 2)

= 1/2

Since it is in the form of p/q, it can be considered as rational number.

√(3/16) = √3/(4 x 4)

= √3/4

Since √3 is a irrational number, dividing irrational number by a rational number we will get an irrational number.

Problem 13 :

Evaluate  √12.25

Solution :

√12.25 = √12.25 x (100/100)

= √(1225 / 100)

= √(1225 / 100)

= √(35 x 35) / (10 x 10)

= 35/10

= 3.5