Simplify the principal square root.

01 / Standard#Your turn

\sqrt{7-4\sqrt3}

Official paper · jm01-2022 · I.4 · PDF 2

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Recognise 7 as 4+3.

Hint 2

Check which sign gives a nonnegative number.

Worked solution

Identify the perfect square.
$7-4\sqrt3=(2-\sqrt3)^2$
Since 2>√3, the principal root is positive.
$\sqrt{(2-\sqrt3)^2}=|2-\sqrt3|=2-\sqrt3$

B: 2−√3.

Checks and common pitfalls: √(u²)=|u|, not automatically u.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Identify the perfect square.
$7-4\sqrt3=(2-\sqrt3)^2$
Since 2>√3, the principal root is positive.
$\sqrt{(2-\sqrt3)^2}=|2-\sqrt3|=2-\sqrt3$

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

2022 JM01