SOLVING SQUARE ROOT EQUATIONS WORKSHEET

In each case, solve for x.

Question 1 :

√x = 5

Question 2 :

√x = -3

Question 3 :

8√x = 16

Question 4 :

√(2x - 1) = 3

Question 5 :

3 + √(2x - 7) = 4

Question 6 :

4 - √(x - 1) = 3

Question 7 :

x = √(x + 2)

Question 8 :

2 - x + √(x + 4) = 0

Question 9 :

8 +3√(3x - 5) = 20

Question 10 :

√(4x - 3) = √(2x + 1)

Question 11 :

3 + √(x - 2) = √(4x + 1)

Question 12 :

If √x + √y = 4√y, where x > 0 and y > 0, what is x in terms of y?

Answers

1. Answer :

√x = 5

Square both sides.

(√x)² = 5²

x = 25

2. Answer :

√x = -3

Square both sides.

(√x)² = (-3)²

x = 9

x = 25

3. Answer :

8√x = 16

Divide both sides by 8.

√x = 2 

Square both sides.

(√x)² = 2²

x = 4

4. Answer :

√(2x - 1) = 3

Square both sides.

[√(2x - 1)]² = 3²

2x - 1 = 9

Add 1 to both sides.

2x = 10

Divide both sides by 2.

x = 5

5. Answer :

3 + √(2x - 7) = 4

Subtract 3 from both sides.

√(2x - 7) = 1

Square both sides.

[√(2x - 7)]² = 1²

2x - 7 = 1

Add 7 to both sides.

2x = 8

Divide both sides by 2.

x = 4

6. Answer :

4 - √(x - 1) = 3

Subtract 4 from both sides.

-√(x - 1) = -1

Square both sides.

[-√(x - 1)]² = (-1)²

x - 1 = 1

Add 1 to both sides.

x = 2

7. Answer :

x = √(x + 2)

Square both sides.

x² = [√(x + 2)]²

x² = x + 2

Subtract x and 2 from both sides.

x² - x - 2 = 0

Factor and solve it.

x² - x - 2 = 0

(x + 1)((x - 2) = 0

x + 1 = 0  or  x - 2 = 0

x = -1  or  x = 2

8. Answer :

2 - x + √(x + 4) = 0

Subtract 2 from both sides.

-x + √(x + 4) = -2

Add x to both sides.

√(x + 4) = x - 2

Square both sides.

[√(x + 4)]² = (x - 2)²

x + 4 = (x - 2)(x - 2)

x + 4 = x² - 2x - 2x + 4

x + 4 = x² - 4x + 4

Subtract x and 4 from both ides.

0 = x² - 5x

or

x² - 5x = 0

x(x - 5) = 0

x = 0  or  x - 5 = 0

x = 0  or  x = 5

9. Answer :

8 +3√(3x - 5) = 20

Subtract 8 from both sides.

3√(3x - 5) = 12

Divide both sides by 3.

√(3x - 5) = 4

Square both sides.

[√(3x - 5)]² = 4²

3x - 5 = 16

Add 5 to both sides.

3x = 21

Divide both sides by 3.

x = 7

10. Answer :

√(4x - 3) = √(2x + 1)

Square both sides.

[√(4x - 3)]² = [√(2x + 1)]²

4x - 3 = 2x + 1

Subtract 2x from both sides.

2x - 3 = 1

Add 3 to both sides.

2x = 4

Divide both sides by 2.

x = 2

11. Answer :

3 + √(x - 2) = √(4x + 1)

Square both sides.

[3 + √(x - 2)]² = [√(4x + 1)]²

[3 + √(x - 2)][3 + √(x - 2)] = 4x + 1

9 + 3√(x - 2) + 3√(x - 2) + (x - 2) = 4x + 1

9 + 6√(x - 2) + x - 2 = 4x + 1

6√(x - 2) + x + 7 = 4x + 1

Subtract x from both sides.

6√(x - 2) + 7 = 3x + 1

Subtract 7 to from both sides.

6√(x - 2) = 3x - 6

6√(x - 2) = 3(x - 2)

Divide both sides by 3.

2√(x - 2) = x - 2

Square both sides.

[2√(x - 2)]² = (x - 2)²

2²[√(x - 2)]² = (x - 2)(x - 2)

4(x - 2) = x² - 2x - 2x + 4

4x - 8 = x² - 4x + 4

Subtract 4x from both sides.

-8 = x² - 8x + 4

Add 8 to both sides.

0 = x² - 8x + 12

or

x² - 8x + 12 = 0

Factor and solve.

(x - 2)(x - 6) = 0

x - 2 = 0  or  x - 6 = 0

x = 2  or  x = 6

12. Answer :

√x + √y = 4√y

Subtract √y from both sides.

√x = 3√y

Square both sides.

[√x]² = [3√y]²

x = 3²(√y)²

x = 9y

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