# Digital SAT Math:Practice Questions-Passport to advanced mathematics-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   Easy

$$\sqrt{m^{2}}=\sqrt{64^{2}}$$

What is the positive solution to the given equation?
A. 4
B. 8
C. 16
D. 64

Ans: D

To solve the equation $$\sqrt{m^{2}} = \sqrt{64^{2}}$$, we need to simplify both sides and find the positive solution.

Left Side

$\sqrt{m^2} = |m|$

The square root of $$m^2$$ is the absolute value of $$m$$, which is $$|m|$$.

Right Side

$\sqrt{64^2} = |64| = 64$
The square root of $$64^2$$ is the absolute value of 64, which is 64.

So, we have:
$|m| = 64$

Since we are looking for the positive solution:
$m = 64$

[Calc]  Question Easy

$\sqrt{x}(\sqrt{x}+\sqrt{y})$

Which of the following expressions is equal to the given expression, where $$x \geq 0$$ and $$y \geq 0$$ ?
A) $$x+\sqrt{x y}$$
B) $$x+\sqrt{x+y}$$
C) $$\sqrt{x^2+x y}$$
D) $$\sqrt{x^2+x+y}$$

A

The given expression is:
$\sqrt{x}(\sqrt{x}+\sqrt{y})$

Distribute $$\sqrt{x}$$:
$\sqrt{x} \cdot \sqrt{x} + \sqrt{x} \cdot \sqrt{y}$
$x + \sqrt{xy}$

So the answer is:
$\boxed{A}$

[Calc]  Question Easy

$$L=S \sqrt{1-\frac{v^2}{c^2}}$$

When the speed of an object approaches the speed of light, its length as seen by an observer changes. When the object is stationary relative to an observer, its length is $S$, and when the same object is moving at speed $v$ relative to the observer, its length is $L$. The formula above expresses $L$ in terms of $S, v$, and $c$, the speed of light. Which of the following gives the speed of the object in terms of the other quantities?
A) $v=c \sqrt{1-\frac{L^2}{S^2}}$
B) $v=c \sqrt{1+\frac{L^2}{S^2}}$
C) $v=c^2\left(1-\frac{L^2}{S^2}\right)$
D) $v=c^2\left(1+\frac{L^2}{S^2}\right)$

A

Question

Which of the following expression is equivalent to $\left(16 x^9 y^3\right)^{\frac{1}{2}}$, where $x \geq 0$ and $y \geq 0$ ?
A. $4 x^3 y^{\frac{3}{2}}$
B. $4 x^{\frac{9}{2}} y^{\frac{3}{2}}$
C. $8 x^3 y^3$
D. $8 x^{\frac{9}{2}} y^3$

Ans: B

Question

If $\sqrt{ } 2 x=8$, what is the value of $x$ ?
A. 4
B. 8
C. 32
D. 64

Ans: C

Questions

$\sqrt{x+28}-2 \sqrt{x+1}=0$

What value of $x$ satisfies the equation above?
A. 8
B. 9
C. 26
D. 27