Cellar SweeperRootkin · roots and radicals

Sweeps every root out of the cellar: dividing roots and rationalizing denominators.

Divide Square Roots

Dividing roots and rationalizing denominators. In MathBound, the free Algebra I adventure game, Cellar Sweeper asks these problems, and the only way past is to solve them.

Part of Radicals and More Functions: chapter 11 of the standard course.

Play this battle free

10 questions, no sign-up, nothing saved. Climbs from the basics to harder questions.

What you will practice

Use Quotient Property. Divide square roots of integers by combining them under a single radical and simplifying.
Rationalize Monomial Denominators. Rationalize a denominator consisting of a single square root by multiplying by a strategic form of 1.
Rationalize Variable Denominators. Rationalize a denominator containing a single variable under a square root.
Rationalize Binomial Denominators. Rationalize a two-term denominator containing a radical by multiplying numerator and denominator by the conjugate.

Worked examples

Made by the game’s own question engine. Try each one, then open its steps.

Example 1 · Use Quotient Property

Divide:

\frac{10 80}{2 5}

$40$
$5$
$20$
$80$

Show the worked steps

$Divide$ $the$ $coefficients:$ $\frac{10}{2} = 5 .$
$Divide$ $the$ $radicals:$ $\frac{80}{5} = 16 = 4 .$
$5 \cdot 4 = 20 .$

Answer: $20$

Example 2 · Rationalize Monomial Denominators

Simplify:

\frac{4}{5 7}

$\frac{4 7}{7}$
$\frac{4 7}{245}$
$\frac{4 7}{35}$
$\frac{4 7}{5}$

Show the worked steps

$Multiply$ $the$ $top$ $and$ $the$ $bottom$ $by$ $7 .$
$The$ $bottom$ $becomes$ $5 \cdot 7 = 35,$ $giving$ $\frac{4 7}{35} .$

Answer: $\frac{4 7}{35}$

Example 3 · Rationalize Variable Denominators

Simplify:

\frac{3}{y}

$\frac{3}{y}$
$\frac{3 y}{y}$
$\frac{3 y}{y ^{2}}$
$3 y$

Show the worked steps

$Multiply$ $the$ $top$ $and$ $the$ $bottom$ $by$ $y .$
$The$ $top$ $becomes$ $3 y$ $and$ $the$ $bottom$ $y : \frac{3 y}{y} .$

Answer: $\frac{3 y}{y}$

Where it is in your textbook

Textbook	Lessons
Standard course	11.2
Big Ideas Math Algebra 1	9.1
Big Ideas Math Algebra 1 (2022)	9.1
enVision Algebra 1	9-3
enVision Algebra 1 (2024)	6-2
Glencoe Algebra 1	10-2
Math Nation Algebra 1 (Florida B.E.S.T.)	1.10
OpenStax Elementary Algebra 2e	9.5
Pearson Algebra 1 Common Core	10-2, 10-3
Reveal Algebra 1	8-5
SpringBoard Algebra 1	20

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