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

Answers

1. Answer :

x² = 25

Take square root on both sides.

√x² = ±√25

x = ±√(5 ⋅ 5) 

x = ±5

x = -5  or  x = 5

2. Answer :

x² - 6 = 3

Add 6 to both sides.

x² = 9

Take square root on both sides.

√x² = ±√9

x = ±3

x = -3  or  x = 3

3. Answer :

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

4. Answer :

2x² - 98 = 0

Add 98 to 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. Answer :

32x² = 2

Divide both sides by 32.

x² = ²⁄₃₂

x² = ¹⁄₁₆

Take square root on both sides.

√x² = ±√¹⁄₁₆

x = ±√(¼ ⋅ ¼)

x = ±¼

x = ⁻¹⁄₄  or  x = ¼

6. Answer :

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

7. Answer :

5x² - 3 = 497

Add 3 to both sides.

5x² = 500

Divide both sides by 5.

x² = 100

Take square root on both sides.

√x² = ±√100

x = ±√(10 ⋅ 10)

x = ±10

x = -10  or  x = 10

8. Answer :

(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

9. Answer :

(x + ¼)² - ¹⁄₁₆ = 0

Add to ¹⁄₁₆ both sides.

(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

10. Answer :

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

11. Answer :

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

12. Answer :

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

13. Answer :

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

14. Answer :

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

15. Answer :

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) + 6² - 6² + 11 = 0

x² - 2(x)(6) + 6² - 36 + 11 = 0

x² - 2(x)(6) + 6² - 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

Add 25 to both sides.

(x - 6)² = 25

Take square root on both sides.

√(x - 6)² = ±√25

x - 6 = ±√(5 ⋅ 5)

x - 6 = ±5

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