# Digital SAT Math Practice Questions – Medium : Radicals and rational exponents

## SAT MAth Practice questions – all topics

• Advanced Math Weightage: 35% Questions: 13-15
• Equivalent expressions
• Nonlinear equations in one variable and systems of equations in two variables
• Nonlinear functions

## SAT MAth and English  – full syllabus practice tests

[Calc]  Question  Medium

$\sqrt{x^2}=5$

What are all possible solutions to the given equation?
A) -25 and 25
B) -5 and 5
C) -25 only
D) 5 only

Ans:B

The given equation is:
$\sqrt{x^2} = 5$

We know that $$\sqrt{x^2} = |x|$$. This means the equation can be rewritten as:
$|x| = 5$

The absolute value equation $$|x| = 5$$ has two possible solutions:
$x = 5 \quad \text{or} \quad x = -5$

[Calc]  Question  medium

If $$5 \sqrt{3 x}-2=13$$, what is the value of $$3 x$$ ?

Ans:9

$$5 \sqrt{3x} – 2 = 13$$

Add 2 to both sides:
$5 \sqrt{3x} = 15$

Divide both sides by 5:
$\sqrt{3x} = 3$

Square both sides to isolate $$3x$$:
$(\sqrt{3x})^2 = 3^2$
$3x = 9$

So, the value of $$3x$$ is $$9$$.

[Calc]  Question   medium

If 3 $$\sqrt{ x − 3} + 10 = 22$$, what is the value of x − 3 ?

16

To solve for $$x – 3$$ in the equation $$3 \sqrt{x – 3} + 10 = 22$$, we first isolate the square root term and then solve for $$x – 3$$.

Subtract $$10$$ from both sides:
$3 \sqrt{x – 3} = 22 – 10$
$3 \sqrt{x – 3} = 12$

Next, divide both sides by $$3$$:
$\sqrt{x – 3} = \frac{12}{3}$
$\sqrt{x – 3} = 4$

Now, to solve for $$x – 3$$, we square both sides of the equation:
$( \sqrt{x – 3} )^2 = 4^2$
$x – 3 = 16$

[Calc]  Question   Medium

$$\sqrt{x^2-9}=4$$

What is the positive solution to the given equation?

5

Questions

. Which of the following is equivalent to $\sqrt[4]{x^2+8 x+16}$, where $x>0$ ?
A. $(x+4)^4$
B. $(x+4)^2$
C. $(x+4)$
D. $(x+4)^{\frac{1}{2}}$

Ans: D

Questions

$\sqrt{x}+4=12$

Which of the following is the solution to the equation above?
A. 8
B. 16
C. 64
D. 140

Ans: C

Questions

$\sqrt[a]{x^b}$

Which of the following is equivalent to the expression above for all $x>0$, where $a$ and $b$ are positive integers?
A. $x^{a b}$
B. $x^{\frac{a}{b}}$
C. $x^{\frac{b}{a}}$
D. $x^{a-b}$

Ans: C

Questions

$\sqrt{x-3}=3-\sqrt{x}$

If $x$ is the solution to the equation above, what is the value of $\sqrt{x-3}$ ?
A. 1
B. $\sqrt{\frac{3}{2}}$
C. $\sqrt{3}$
D. 3

Ans: A

Questions

$(3+4 i)-(2+3 i)$

In the complex number system, which of the following is equivalent to the expression above? (Note: $i=\sqrt{-1}$ )
A. 0
B. $1+i$
C. $-1-i$
D. $-5-7 I$

Ans: B

Questions

$Q=\sqrt{\frac{2 d K}{h}}$

The formula above is used to estimate the ideal quantity, $Q$, of items a store manager needs to order given the demand quantity, $d$, the set up cost per order, $K$, and the storage cost per item, $h$. Which of the following correctly expresses the storage cost per item in terms of the other variables?
A. $h=\sqrt{\frac{2 d K}{Q}}$
B. $h=\frac{\sqrt{2 d K}}{Q}$
C. $h=\frac{2 d K}{Q^2}$
D. $h=\frac{Q^2}{2 d K}$