Square Roots · Meet square roots · 1.2

The radical symbol.

The symbol √ is the radical sign; the number under it is the radicand. √49 means “the (positive) number whose square is 49”, which is 7.

01 / THE IDEA

See it work.

Watch the method

The radical symbol

√49 = 7 — the radicand is 49.

1 / 2
49\sqrt{49}
1

Ask the question

√49 asks: what number squared gives 49?

49=?\sqrt{49} = ?
2

Find the root

7² = 49, so √49 = 7.

49=7\sqrt{49} = 7
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.

Reading a radical

The radical sign √ takes the principal (non-negative) square root of the radicand underneath it.

Why it works

√49 reads “root forty-nine” = 7.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Evaluate √81

1

Ask the question

√81 asks: what number squared gives 81? √81 = ?

2

Find the root

9² = 81, so √81 = 9. √81 = 9

EX 2medium

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

EX 3hard

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

04 / COMMON TRAPS

Where students slip.

Trap

Calling the whole thing the radicand.

Fix

The radicand is just the number under the √.

Trap

Giving the negative root.

Fix

The √ symbol means the non-negative root.

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 √16

Need a hint?
  • The radicand is under the √ sign.
  • Find the non-negative root.
C2

Evaluate √36

Need a hint?
  • The radicand is under the √ sign.
  • Find the non-negative root.
C3

Evaluate √100

Need a hint?
  • The radicand is under the √ sign.
  • Find the non-negative root.
C4

Evaluate √100

Need a hint?
  • The radicand is under the √ sign.
  • Find the non-negative root.
Apply

Apply (4)

A1

Evaluate √36

Need a hint?
  • The radicand is under the √ sign.
  • Find the non-negative root.
A2

Evaluate √9

Need a hint?
  • The radicand is under the √ sign.
  • Find the non-negative root.
A3

Evaluate √49

Need a hint?
  • The radicand is under the √ sign.
  • Find the non-negative root.
A4

Evaluate √121

Need a hint?
  • The radicand is under the √ sign.
  • Find the non-negative root.
Extension

Extension (4)

E1

Evaluate √49

Need a hint?
  • The radicand is under the √ sign.
  • Find the non-negative root.
E2

Evaluate √144

Need a hint?
  • The radicand is under the √ sign.
  • Find the non-negative root.
E3

Evaluate √144

Need a hint?
  • The radicand is under the √ sign.
  • Find the non-negative root.
E4

Evaluate √100

Need a hint?
  • The radicand is under the √ sign.
  • Find the non-negative root.