PROBLEMS INVOLVING SQUARE ROOTS WORKSHEET FOR SAT

Problem 1 :

In the equation y - y - √(4x2 + 28) = 0, x > 0 and y = 8. What is the value of x ?

A)  3   B)  4    C)  5   D)  6

Solution

Problem 2 :

√(2k2 + 17) - x = 0

If k > 0 and x = 7 in the equation above, what is the value of k ?

A)  2     B)  3      C)  4       D) 5 

Solution

Problem 3 :

√(x - a) = x - 4

If a = 2, what is the solution set of the equation ?

A)  {3, 6}     B)  {2}      C)  {3}       D) {6}

Solution

Problem 4 :

The expression

where a and b are positive constants and x > 1, find the value of a + b.

Solution

Problem 5 :

√(k + 2) - x = 0

In the equation above k is a constant. If x = 9, what is the value of k ?

A)  1     B)  7      C)  16       D) 79

Solution

Problem 6 :

If √x + √9 = √64, find the value of x.

A)  √5      B)  5     C)  25    D)  55

Solution

Problem 7 :

If √(2x + 6) + 4 = x + 3

What is the solution set of equation above ?

A)  {-1}   B)  {5}    C)  {-1, 5}     D)  {0, -1, 5}

Solution

Problem 8 :

If k = 1, which of the following is the solution set of

x - 7 = √(x - k) ?

A)  1    B)  5     C)  10    D) 5, 10

Solution

Problem 9 :

If √49 = √y - √16,  what is the value of y ?

A)  121    B)  65     C)  11    D) √11

Solution

Problem 10 :

√(c - 1) - t = 0

In the equation above, c is a constant. If t = 4, what is the value of c ?

A)  17     B)  15    C)  5     D)  3

Solution

Problem 11 :

a - 6 = √(8a - 7) - 4

What is the solution set of the equation above ?

A)  0   B)  1    C)  11   D)  1, 11

Solution

Answer Key

1)  3, option A is correct.

2) the value of k is 4, option C

3)  x = 6 and x = 3, option A

4) 361/8

5)  x = 79, option D

6)  x = 25

7)  x = 5 and x = -1, option C

8)  x = 10 and x = 5

9)  y = 121

10)  c = 17

11) So, the solution are 1 and 11.

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