Question 1

Let $a$ represent a non-zero rational number and let $b$ represent an irrational number.

Which expression could represent a rational number?

Accepted Answer

$b^2$

Answer

$ab$

Answer

$a+b$

Answer

$-b$

Question 2

Let $a$ represent a non-zero rational number and let $b$ represent an irrational number.

Consider a quadratic equation with integer coefficients and two distinct zeros.
If one zero is irrational, which statement is true about the other zero?

Accepted Answer

The other zero must be irrational.

Answer

The other zero must be non-real.

Answer

The other zero can be either rational or irrational.

Answer

The other zero must be rational.

Question 3

Given that $x>0$, which expression is equivalent to $5\sqrt{xy}+25\sqrt x$?

Accepted Answer

$5x^{\frac{1}{2}}\Big(y^{\frac{1}{2}}+5\Big)$

Answer

$25x^{\frac{1}{2}}(\sqrt y+5)$

Answer

$5(xy)^{-1}+25x^{-1}$

Answer

$\sqrt x\Big(25y^{\frac{1}{2}}+5\Big)$

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