# SQUARE ROOT OF A NUMBER WORKSHEET

Problems 1-9 : In each case, evaluate the square root by prime factorisation :

Problem 1 :

√4

Problem 2 :

√49

Problem 3 :

√18

Problem 4 :

√81

Problem 5 :

√92

Problem 6 :

√0.25

Problem 7 :

√2.25

Problem 8 :

√0.09

Problem 9 :

√0.0001

Problems 10-11 : Evaluate the square root using long division :

Problem 10 :

√288369

Problem 11 :

√459684

Problems 12-20 : Solve for x.

Problem 12 :

x2 = 4

Problem 13 :

x2 - 5 = -5

Problem 14 :

4x2 = 256

Problem 15 :

25x2 = 4

Problem 16 :

x2 + 1.8 = 2.29

Problem 17 :

(7x2 + 3)/2 = 15.5

Problem 18 :

1 - 2x2 = -287

Problem 19 :

(x + 5)2 = 4

Problem 20 :

3(3x - 2)2 = 147

√4 = √(2 ⋅ 2)

= 2

√49 = √(7 ⋅ 7)

= 7

√18 = √(2 ⋅ 3 ⋅ 3)

= 3√2

√81 = √(3 ⋅ 3 ⋅ 3 ⋅ 3)

= 3 ⋅ 3

= 9

√92 = √(2 ⋅ 2 ⋅ 23)

= 2√23

√0.25

Inside the square root, there is a decimal number. To get rid of the decimal point, 0.25 can be written as a fraction. In 0.25, since there are two digits after the decimal point, it can be written as a fraction with denominator 100.

√0.25 = √²⁵⁄₁₀₀

= √(⁵⁄₁₀ ⋅ ⁵⁄₁₀)

⁵⁄₁₀

= 0.5

√2.25 = √²²⁵⁄₁₀₀

= √(¹⁵⁄₁₀ ⋅ ¹⁵⁄₁₀)

¹⁵⁄₁₀

= 1.5

√0.09 = √⁹⁄₁₀₀

= √(³⁄₁₀ ⋅ ³⁄₁₀)

³⁄₁₀

= 0.3

√0.0001 = √¹⁄₁₀₀₀₀

= √(¹⁄₁₀₀ ⋅ ¹⁄₁₀₀)

¹⁄₁₀₀

= 0.01

√288369 = 537

Click here to get step by step guide on finding square root of a number by long division method.

√459684 = 678

To get rid of the square on the left side, take square root on both sides.

√x2 = ±√4

x = ±√(2 ⋅ 2)

x = ±2

x = -2  or  x = 2

x2 - 5 = -5

x2 = 0

Take square root on both sides.

x2 = ±√0

x = 0

4x2 = 256

Divide both sides by 4.

x2 = 64

Take square root on both sides.

√x2 = ±√64

x = ±√(8 ⋅ 8)

x = ±8

x = -8  or  y = 8

25x2 = 4

Divide both sides by 36.

x2 = ⁴⁄₂₅

Take square root on both sides.

√x2 = ±√⁴⁄₂₅

x = ±√(⅖ ⋅ )

x = ±

x = -  or  x =

x2 + 1.8 = 2.29

Subtract 1.8 from both sides.

x2 = 0.49

x2 = ⁴⁹⁄₁₀₀

Take square root on both sides.

√x2 = ±√⁴⁹⁄₁₀₀

x = ±√(⁷⁄₁₀ ⋅ ⁷⁄₁₀)

x = ±⁷⁄₁₀

x = -⁷⁄₁₀  or  x = ⁷⁄₁₀

(7x2 + 3)/2 = 15.5

Multiply both sides by 2.

7x2 + 3 = 31

Subtract 3 from both sides.

7x2 = 28

Divide both sides by 7.

x2 = 4

Take square root on both sides.

√x2 = ±√4

x = ±√(2 ⋅ 2)

x = ±2

x = -2  or  x = 2

1 - 2x2 = -287

Subtract 1 from both sides.

-2x2 = -288

Divide both sides by -2.

x2 = 144

Take square root on both sides.

√x2 = ±√144

x = ±√(12 ⋅ 12)

x = ±12

x = -12  or  x = 12

(x + 5)2 = 4

Take square root on both sides.

√(x + 5)2 = ±√4

x + 5 = ±2

 x + 5 = -2x = -7 x + 5 = 2x = -3

3(3x - 2)2 = 147

Divide both sides by 3.

(3x - 2)2 = 49

Take square root on both sides.

(3x - 2)2 = ±√49

3x - 2 = ±7

 3x - 2 = -73x = -5x = ⁻⁵⁄₃ 3x - 2 = 73x = 9x = 3

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