SAT PRACTICE TEST QUESTIONS ON SQUARE AND SQUARE ROOTS

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 >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

Problem 1 :

If a^-1/2 = 3, what is the value of a ?

a)  -9    b)  1/9     c)  1/3      d)  9

Solution

Problem 2 :

Let n = 1²  + 1⁴ + 1⁶ + 1⁸ + ........ + 1⁵⁰

what is the value of n ?

a)  10     b)  20    c)  25      d)  30

Solution

Problem 3 :

If 4^{2n + 3} = 8^{n + 5}

what is the value of n ?

a)  6     b)  7    c)  8      d)  9

Solution

Problem 4 :

If 2^x/2^y = 2³, then x must equal

a)  y + 3     b)  y - 3      c)  3 - y       d)  3y

Solution

Problem 5 :

If 3^x = 10, what is the value of 3^{x - 3} ?

a)  10/3     b)  10/9      c)  10/27       d)  27/10

Solution

Problem 6 :

If x² y³ = 10 and x³y² = 8, what is the value of x⁵y⁵ ?

a)  18    b)  20      c)  40       d) 80

Solution

Problem 7 :

If a and b are positive even integers, which of the following is greatest ?

a)  (-2a)^b       b)  (-2a)^2b       c)  (2a)^b        d)  2a^2b

Solution

Problem 8 :

Which of the following is equivalent to x^2a/b, for all values of x ?

Solution

Problem 9 :

If x² = y³, for what value of z does x^3z = y⁹ ?

a)  -1       b)  0       c)  1        d)  2

Solution

Problem 10 :

If 2^x+3 - 2^x = k(2^x), what is the value of k ?

a)  3       b)  5       c)  7        d)  8

Solution

Problem 11 :

If 

a)  1/2       b)  3/4       c)  1        d)  4/3

Solution

Problem 12 :

2(√x + 2) = 3√2

If x > 0 in the equation above, what is the value of x ?

a)  2.5    b)  3    c)  3.5      d)  4

Solution

Problem 13 :

If x^ac  ⋅ x^bc = x³⁰, x > 1 and a + b = 5, what is the vale of c?

a)  3    b)  5    c)  6      d)  10

Solution

Problem 14 :

If n³ = x and n⁴ = 20x, where n > 0, what is the value of x ?

Solution

Problem 15 :

If x⁸ y⁷ = 333 and x⁷y⁶ = 3, what is the value of xy ?

Solution