# SQUARE ROOT PROPERTY WORKSHEET

In each case, solve for x using square root property :

Question 1 :

x2 = 25

Question 2 :

x2 - 6 = 3

Question 3 :

2x2 + 5 = 5

Question 4 :

2x2 - 98 = 0

Question 5 :

32x2 = 2

Question 6 :

x2 - 3 = 14

Question 7 :

5x2 - 3 = 497

Question 8 :

(2x2 + 1)/3 = 29

Question 9 :

(x + ¼)2 - ¹⁄₁₆ = 0

Question 10 :

7x2 + 5 = 2280

Question 11 :

x2 + 4 = 0

Question 12 :

5 - 2x2 = -93

Question 13 :

5 - 3x2 = 80

Question 14 :

x2 + 8x + 16 = 0

Question 15 :

x2 - 12x + 11 = 0 x2 = 25

Take square root on both sides.

x2 = ±√25

x = ±√(5 ⋅ 5)

x = ±5

x = -5  or  x = 5

x2 - 6 = 3

x2 = 9

Take square root on both sides.

√x2 = ±√9

x = ±3

x = -3  or  x = 3

2x2 + 5 = 5

Subtract 5 from both sides.

2x2 = 0

Divide both sides by 2.

x2 = 0

Take square root on both sides.

√x2 = ±√0

x = 0

2x2 - 98 = 0

2x2 = 98

Divide both sides by 2.

x2 = 49

Take square root on both sides.

√x2 = ±√49

x = ±√(7 ⋅ 7)

x = ±7

x = -7  or  x = 7

32x2 = 2

Divide both sides by 32.

x2 = ²⁄₃₂

x¹⁄₁₆

Take square root on both sides.

√x2 = ±√¹⁄₁₆

x = ±√(¼ ⋅ ¼)

x = ±¼

x = ⁻¹⁄₄  or  x = ¼

x2 + 3 = 14

Subtract 3 from both sides.

x2 = 11

Take square root on both sides.

√x2 = ±√11

x = ±√11

x = -√11  or  x = √11

5x2 - 3 = 497

5x2 = 500

Divide both sides by 5.

x= 100

Take square root on both sides.

√x2 = ±√100

x = ±√(10 ⋅ 10)

x = ±10

x = -10  or  x = 10

(2x2 + 1)/5 = 11

Multiply both sides by 5.

2x2 + 1 = 55

Subtract 1 from both sides.

2x2 = 54

Divide both sides by 2.

x2 = 27

Take square root on both sides.

√x2 = ±√27

x = ±√(3 ⋅ 3 ⋅ 3)

x = ±3√3

x = -3√3  or  x = 3√3

(x + ¼)2 - ¹⁄₁₆ = 0

(x + ¼)2 = ¹⁄₁₆

Take square root on both sides.

(x + ¼)2 = ±√¹⁄₁₆

x + ¼ = ±√(¼ ⋅ ¼)

x + ¼ ±¼

x + ¼ = ±¼

x + ¼ = ⁻¼  or  x + ¼ = ¼

 x + ¼ = ⁻¹⁄₄x = ⁻¹⁄₄ ⁻ ¼x = ⁻²⁄₄x = ⁻¹⁄₂ x + ¼ = ¹⁄₄x = ¹⁄₄ ⁻ ¼x = 0

7x2 + 5 = 2280

Subtract 5 from both sides.

7x2 = 2275

Divide both sides by 7.

x2 = 325

Take square root on both sides.

√x2 = ±√325

x = ±√(5 ⋅ 5 ⋅ 13)

x = ±5√13

x = -5√13  or  x = 5√13

x2 + 4 = 0

Subtract 8 from both sides.

x2 = -4

Take square root on both sides.

√x2 = ±√-4

x = ±√(-1 ⋅ 4)

x = ±√(i2 ⋅ 2 ⋅ 2)

x = ±2i

x = -2i  or  x = 2i

5 - 2x2 = -93

Subtract 5 from both sides.

-2x2 = -98

Divide both sides by -2.

x2 = 49

Take square root on both sides.

√x2 = ±√49

x = ±√(7 ⋅ 7)

x = ±7

x = -7  or  x = 7

5 - 3x2 = 80

Subtract 5 from both sides.

-3x2 = 75

Divide both sides by -3.

x2 = -25

Take square root on both sides.

√x2 = ±√-25

x = ±√(-1 ⋅ 25)

x = ±√(-1 ⋅ 5 ⋅ 5)

x = ±√(i2 ⋅ 5 ⋅ 5)

x = ±5i

x = -5i  or  x = 5i

x2 + 8x + 16 = 0

Rewrite x2 + 8x + 16 in the form of a2 + 2ab + b2.

x2 + 2(x)(4) + 42 = 0

We can use the algebraic identity (a + b)2 a2 + 2ab + b2  to write the expression on the left side in terms of square of a binomial.

(x + 4)2 = 0

Take square root on both sides.

(x + 4)2 = ±√0

x + 4 = 0

x = -4

x2 - 12x + 11 = 0

Rewrite x2 - 12x + 61 in the form of a2 - 2ab + b2.

x2 - 2(x)(6) + 11 = 0

x2 - 2(x)(6) + 6- 6+ 11 = 0

x2 - 2(x)(6) + 6- 36 + 11 = 0

x2 - 2(x)(6) + 6- 25 = 0

We can use the algebraic identity (a - b)2 a2 - 2ab + b2  to write the expression on the left side in terms of square of a binomial.

(x - 6)2 - 25 = 0

(x - 6)2 = 25

Take square root on both sides.

(x - 6)2 = ±√25

x - 6 = ±√(5 ⋅ 5)

x - 6 = ±5

 x - 6 = -5x = 1 x - 6 = 5x = 11

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