Step: 1

[Original equation.]

Step: 2

[Apply square root on both sides.]

Step: 3

= ±( 1 9 × 1 9 )

[If y ^{2} = z , then y = ±z .]

Step: 4

= ± 19

Step: 5

So, + 19 and - 19 are the two integers that satisfy the equation.

Correct Answer is : + 19 and - 19

Step: 1

Area of a square field = (side)^{2}

Step: 2

side = A r e a

Step: 3

= 2 1 1 6

[Substitute.]

Step: 4

= 4 6 × 4 6 = 46

[Write 2116 as 46 × 46 and simplify.]

Step: 5

The perimeter of the square field = 4 × (side of the square field)

Step: 6

= 4 × 46 = 184

[Substitute and multiply.]

Step: 7

Cost of fencing the field = (Perimeter of the field) × (Cost of fencing per ft)

Step: 8

= 184 × 4 = 736

[Substitute and multiply.]

Step: 9

So, the cost of fencing the field is $736.

Correct Answer is : $736

Step: 1

Area = length x width

[Formula.]

Step: 2

= 8√3 x 8√3

[Substitute the value of length and width.]

Step: 3

= 64 x 3

[Simplify.]

Step: 4

= 192

[Multiply.]

Step: 5

The area of the figure is 192 square units.

Correct Answer is : 192 square units

Step: 1

The area of the square = (side)^{2}

[Formula.]

Step: 2

The side of the square = √(area of the square)

Step: 3

= √12

[Substitute the area of the square as 12.]

Step: 4

= √(2 x 2 x 3)

[Write 12 as a product of prime factors.]

Step: 5

= 2√3

[Find the square root.]

Step: 6

The side of the square with an area of 12 square units is 2√3 units.

Correct Answer is : 2√3

Step: 1

-y ^{2} = -1369

[Original equation.]

Step: 2

[Divide each side by -1.]

Step: 3

[Apply square roots to each side.]

Step: 4

= ± 37

[Find the square root.]

Step: 5

The two integers that satisfy the equation -y ^{2} = -1369 are 37 and -37.

Correct Answer is : 37 and -37

Step: 1

Let n be the side of the square floor.

Step: 2

The area of a square = side × side.

Step: 3

196 = n × n

[Substitute the values.]

Step: 4

[Multiply.]

Step: 5

√n ^{2} = √196

[Square root each side.]

Step: 6

[Find the positive square root, since the side-length cannot be negative.]

Step: 7

The side-length of the square floor is 14 meters.

Correct Answer is : 14 m

Step: 1

The area of the school is in the form of square.

Step: 2

The area of the school = 22500 ft^{2}

Step: 3

The side of the school = 2 2 5 0 0

[The side of square = a r e a o f t h e s q u a r e .]

Step: 4

= 1 5 0 × 1 5 0

[Write 22500 as perfect square.]

Step: 5

= 150

[Simplify.]

Step: 6

The perimeter of the school = 4 × 150

[The perimeter of the square = 4 × side of a square.]

Step: 7

= 600 ft.

[Simplify.]

Step: 8

The perimeter of the school is 600 ft.

Correct Answer is : 600 ft

Step: 1

Units place digit is a square of a first odd prime number = 3^{2} = 9.

Step: 2

10's place digit is a square root of a perfect square between 34 and 43 = 3 6 = 6.

Step: 3

The three digit number is a perfect square.

Step: 4

So, the 3 digit number is 169.

Correct Answer is : 169

Step: 1

Let n be the side of the square floor.

Step: 2

The area of a square = side × side.

Step: 3

256 = n × n

[Substitute the values.]

Step: 4

[Multiply.]

Step: 5

[Square root each side.]

Step: 6

[Find the positive square root, since the side-length cannot be negative.]

Step: 7

The side-length of the square floor is 16 meters.

Correct Answer is : 16 m

Step: 1

Units place digit is a square of a first odd prime number = 3^{2} = 9.

Step: 2

10's place digit is a square root of a perfect square between 35 and 43 = 3 6 = 6.

Step: 3

The three digit number is a perfect square.

Step: 4

So, the 3 digit number is 169.

Correct Answer is : 169

Step: 1

The length of Laura's old garden = 9 m

Step: 2

Area of garden = 9 × 9 = 81

[area of a square = side^{2}]

Step: 3

Area of Laura's new garden = 1 5 of the area of the old garden

Step: 4

Step: 5

Side length of the new garden = a r e a = 1 6 . 2 = 4.02

[side = a r e a ]

Correct Answer is : 4.02 m

Step: 1

The perfect square nearer to 146 is 144.

Step: 2

[1 4 4 = 12]

Step: 3

The perfect square nearer to 62 is 64.

Step: 4

[6 4 = 8]

Step: 5

The perfect square nearer to 8 is 9.

Step: 6

[9 = 3]

Step: 7

The perfect square nearer to 98 is 100.

Step: 8

[1 0 0 = 10]

Step: 9

So, the point P represents 9 8 on the number line.

Correct Answer is : 9 8

Step: 1

Area of the square = side^{2} = 16 square inches

[Given.]

Step: 2

Side = 4 inches

[Take square root on both sides of the equation and simplify.]

Step: 3

Double the length of the side = 2 × 4 inches = 8 inches

Step: 4

The area of the new square = 8 in. × 8 in. = 64 in.^{2}

Correct Answer is : 64 square inches

Step: 1

The point on the line lies between 0 and - 5 .

Step: 2

Among the choices - 6 , - 8 lie between 0 and - 5.

[The point lie left to the 0 on the number line.]

Step: 3

The point on the number line is closer to 0.

Step: 4

Among the choices the approximate value of - 6 is closer to 0.

Step: 5

So, the point on the number line represents - 6 .

Correct Answer is : - 6

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- Square Root