PROBLEMS INVOLVING SQUARE ROOTS FOR DIGITAL SAT PRACTICE

Problem 1 :

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:

√x + √y = 4√y

√x = 4√y - √y

√x = 3√y

Taking square on both sides,

x = 9y

So, option (B) is correct.

Problem 2 :

What is one possible value of x for which the function g above is undefined?

Solution:

(x - 1)(x - 2) ≥ 0

x - 1 ≥ 0, x - 2 ≥ 0

x ≥ 1, x ≥ 2

x ≥ 2

(x - 1)(x - 2) ≤ 0

x - 1 ≤ 0, x - 2 ≤ 0

x ≤ 1, x ≤ 2

x ≤ 1

So, its defined on the interval (-∞, 1] ∪ [2, +∞).

So, its undefined when (1, 2).

One possible value of x as 1.5.

Problem 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:

So, option (B) is correct.

Problem 4 :

Solution:

Problem 5 :

Solution:

So, option (C) is correct.

Problem 6 :

What is the solution set for the equation above?

Solution:

So, option (C) is correct.

Problem 7 :

If a = 5√2 and 2a = √2x, what is the value of x?

Solution:

2a = √2x

a = 5√2

2(5√2) = √2x

10√2 = √2x

Taking square on both sides,

(10√2)² = (√2x)²

100 × 2 = 2x

200 = 2x

x = 100

Problem 8 :

The given equation relates the distinct positive real numbers w, x and y. Which equation correctly expresses w in terms of x and y?

Solution:

So, option (C) is correct.

Problem 9 :

If x ≠ 0, for what real value of x is the equation above true?

Solution:

Problem 10 :

A right triangle has sides of length 2√2, 6√2 and √80 units. What is the area of the triangle, in square units?

A) 8√2 + √80      B) 12       C) 24√80          D) 24

Solution:

So, option (B) is correct.

Problem 11 :

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

Solution:

Problem 12 : 

For what value of x is the function g above undefined?

Solution:

Applying x = 71, we get

For x = 71, the function g(x) is undefined.

Problem 13 :

A) 0        B) 2           C) 6      D) 12

Solution:

So, option (D) is correct.