Simplify the radical expression exactly.

01 / Standard#Your turn

\frac{\sqrt{140}-\sqrt{132}}{\sqrt{35}+\sqrt{33}}

Official paper · jm01-2021 · I.14 · PDF 3

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Factor 4 from each radicand in the numerator.

Hint 2

Rationalize with √35−√33.

Worked solution

Simplify the numerator before rationalizing.
$\frac{2(\sqrt{35}-\sqrt{33})}{\sqrt{35}+\sqrt{33}}$
The conjugate denominator is 35−33=2.
$\frac{2(\sqrt{35}-\sqrt{33})^2}{35-33}=68-2\sqrt{1155}$

A: 68−2√1155.

Checks and common pitfalls: Keep the cross term −2√(35·33) when squaring.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Simplify the numerator before rationalizing.
$\frac{2(\sqrt{35}-\sqrt{33})}{\sqrt{35}+\sqrt{33}}$
The conjugate denominator is 35−33=2.
$\frac{2(\sqrt{35}-\sqrt{33})^2}{35-33}=68-2\sqrt{1155}$

Think first. Reveal a hint when the class is ready.

2021 JM01