Square Roots · Meet square roots · 1.4

Perfect squares.

A perfect square is a whole number times itself: 1, 4, 9, 16, 25, … 144. Their square roots are whole numbers. Knowing them by heart makes roots fast.

01 / THE IDEA

See it work.

Watch the method

Perfect squares

√64 = 8 — 64 is a perfect square.

1 / 2
64\sqrt{64}
1

Ask the question

√64 asks: what number squared gives 64?

64=?\sqrt{64} = ?
2

Find the root

8² = 64, so √64 = 8.

64=8\sqrt{64} = 8
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.

Know them by heart

The perfect squares up to 144 are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 — the squares of 1–12.

Why it works

8² = 64, so √64 = 8.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

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 2medium

Evaluate √144

1

Ask the question

√144 asks: what number squared gives 144? √144 = ?

2

Find the root

12² = 144, so √144 = 12. √144 = 12

EX 3hard

Evaluate √121

1

Ask the question

√121 asks: what number squared gives 121? √121 = ?

2

Find the root

11² = 121, so √121 = 11. √121 = 11

04 / COMMON TRAPS

Where students slip.

Trap

Thinking every number is a perfect square.

Fix

Only 1, 4, 9, 16, … are; √20 is not whole.

Trap

Mixing up 64 and 8.

Fix

8 is the root; 64 is the square.

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?
  • Match the radicand to a square of 1–12.
  • Recall the squares list.
C2

Evaluate √64

Need a hint?
  • Match the radicand to a square of 1–12.
  • Recall the squares list.
C3

Evaluate √49

Need a hint?
  • Match the radicand to a square of 1–12.
  • Recall the squares list.
C4

Evaluate √121

Need a hint?
  • Match the radicand to a square of 1–12.
  • Recall the squares list.
Apply

Apply (4)

A1

Evaluate √49

Need a hint?
  • Match the radicand to a square of 1–12.
  • Recall the squares list.
A2

Evaluate √25

Need a hint?
  • Match the radicand to a square of 1–12.
  • Recall the squares list.
A3

Evaluate √144

Need a hint?
  • Match the radicand to a square of 1–12.
  • Recall the squares list.
A4

Evaluate √121

Need a hint?
  • Match the radicand to a square of 1–12.
  • Recall the squares list.
Extension

Extension (4)

E1

Evaluate √64

Need a hint?
  • Match the radicand to a square of 1–12.
  • Recall the squares list.
E2

Evaluate √49

Need a hint?
  • Match the radicand to a square of 1–12.
  • Recall the squares list.
E3

Evaluate √9

Need a hint?
  • Match the radicand to a square of 1–12.
  • Recall the squares list.
E4

Evaluate √4

Need a hint?
  • Match the radicand to a square of 1–12.
  • Recall the squares list.