Mrs.D Math · 8th Grade

ROOT
RADAR

Estimating Square Roots · The Number System
🔱 Square Roots
🌀 Irrational Numbers
✅ Rational Numbers
⚡ √64 = 8
📡 6 < √40 < 7
🎯 √50 ≈ 7.1
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📚 Estimating Square Roots

Know Your Perfect Squares

A perfect square has a whole-number square root. These are your landmarks!

√1=1√4=2√9=3√16=4√25=5√36=6√49=7√64=8√81=9√100=10√121=11√144=12√169=13√196=14√225=15√400=20

The Sandwich Method — What Is It Between?

1
Find the perfect square just BELOW your number.
For √40 → 36 is just below
2
Find the perfect square just ABOVE your number.
For √40 → 49 is just above
3
Take the square roots of both. Your answer is sandwiched between them!
√36 < √40 < √49  →  6 < √40 < 7

Finding the Closest Estimate

1
Sandwich it first: √50 is between 7 and 8 (since 49 < 50 < 64).
2
Check which perfect square is closer. 50 is only 1 away from 49, but 14 away from 64.
√50 ≈ 7  (just barely over → ≈ 7.1)
3
Why it matters: √50 is irrational — its decimal never ends and never repeats. Estimating tells you where it lives on the number line.

How to Play

↔️
Between — Pick the two consecutive whole numbers the square root falls between.
🎯
Closest — Choose the closest whole number (or the nearest tenth on Hard!).
🌀
Mixed — Both types together for the ultimate challenge!
🧮
Calculator tip: Try each one WITHOUT your calculator first — then use it to check yourself. That’s how estimation skills stick!
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