SOLVING RADICAL EQUATIONS PRACTICE FOR SAT

Question 1 :

√ab = a-b

If a > 0 and b > 0, the equation above is equivalent to which of the following ?

(a)  ab = a²-b²   (b) ab = a²+b²

(c)  2ab - a²-b²  (d) 3ab = a²+b²

Solution

Question 2 :

Solve for x, when x > 0

(x + 3)² = 121

Solution

Question 3 :

If √x + √9 = √64, what is the value of x ?

(a)  √5  (b)  5  (c)  25  (d)  55

Solution

Question 4 :

√(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

Question 5 :

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

(a)  16y   (b)  9y   (c)  6y   (d)  4y

Solution

Question 6 :

√(2x²-14)/a = 3

If x > 0 and a = 2 in the equation above, what is the value of x ?

(a)  4   (b)  5   (c)  6   (d)  7

Solution

Question 7 :

If x > 0 and 9x² = 40, which of the following is equivalent to the value of x ?

(a)  (40/9)²   (b)  √40/9   (c)  √9/40   (d)  √(40/9)

Solution

Question 8 :

If m = 1/√n, where m > 0 and n > 0, what is n in terms of m ?

(a)  n = 1/√m   (b)  n = 1/m   (c)  n = 1/m²   (d)  n = m²

Solution

Question 9 :

If √(4+√x) = 1 + √3, what is the value of x ?

(a)  0   (b)  2   (c)  6   (d)  12

Solution

Question 10 :

If 3√x³ = √72, what is the value of x ?

Solution

Question 11 :

In the equation (ax + 3)² = 36 , a is a constant. If x = −3 is one solution to the equation, what is a possible value of a ?

a) −11   b) −5    c) −1    d) 0

Solution

Question 12 :

√(2x+6) + 4 = x + 3

 What is the solution set of the equation above?

a) {−1}   b) {5}   c) {−1, 5}    d) {0, −1, 5}

Solution