Square Roots · Evaluate & estimate · 2.1

Roots of perfect squares.

Evaluating a perfect-square root means recalling which whole number squared gives the radicand. √81 = 9. Practice the squares of 1–12 until it’s instant.

01 / THE IDEA

See it work.

Watch the method

Roots of perfect squares

√81 = 9 because 9² = 81.

1 / 2
81\sqrt{81}
1

Ask the question

√81 asks: what number squared gives 81?

81=?\sqrt{81} = ?
2

Find the root

9² = 81, so √81 = 9.

81=9\sqrt{81} = 9
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a number.

streak 0
best 0
… =
— / WHY IT WORKS

The idea underneath.

Instant recall

Each perfect square has exactly one non-negative root; memorising the table makes evaluation immediate.

Why it works

√100 = 10, √121 = 11.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Evaluate √16

1

Ask the question

√16 asks: what number squared gives 16? √16 = ?

2

Find the root

4² = 16, so √16 = 4. √16 = 4

EX 2medium

Evaluate √9

1

Ask the question

√9 asks: what number squared gives 9? √9 = ?

2

Find the root

3² = 9, so √9 = 3. √9 = 3

EX 3hard

Evaluate √4

1

Ask the question

√4 asks: what number squared gives 4? √4 = ?

2

Find the root

2² = 4, so √4 = 2. √4 = 2

04 / COMMON TRAPS

Where students slip.

Trap

Guessing instead of recalling.

Fix

Learn the squares of 1–12.

Trap

Off-by-one (√81 = 8).

Fix

9² = 81, not 8².

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Evaluate √25

Need a hint?
  • Which number squared gives the radicand?
  • Use the squares of 1–12.
C2

Evaluate √49

Need a hint?
  • Which number squared gives the radicand?
  • Use the squares of 1–12.
C3

Evaluate √9

Need a hint?
  • Which number squared gives the radicand?
  • Use the squares of 1–12.
C4

Evaluate √81

Need a hint?
  • Which number squared gives the radicand?
  • Use the squares of 1–12.
Apply

Apply (4)

A1

Evaluate √81

Need a hint?
  • Which number squared gives the radicand?
  • Use the squares of 1–12.
A2

Evaluate √81

Need a hint?
  • Which number squared gives the radicand?
  • Use the squares of 1–12.
A3

Evaluate √144

Need a hint?
  • Which number squared gives the radicand?
  • Use the squares of 1–12.
A4

Evaluate √36

Need a hint?
  • Which number squared gives the radicand?
  • Use the squares of 1–12.
Extension

Extension (4)

E1

Evaluate √4

Need a hint?
  • Which number squared gives the radicand?
  • Use the squares of 1–12.
E2

Evaluate √64

Need a hint?
  • Which number squared gives the radicand?
  • Use the squares of 1–12.
E3

Evaluate √144

Need a hint?
  • Which number squared gives the radicand?
  • Use the squares of 1–12.
E4

Evaluate √121

Need a hint?
  • Which number squared gives the radicand?
  • Use the squares of 1–12.