Square Roots · Meet square roots · 1.1

Squaring & its inverse.

Squaring a number multiplies it by itself: 5² = 25. The square root undoes that: √25 = 5, because 5² = 25. A square root asks “what number, squared, gives this?”

01 / THE IDEA

See it work.

The area model

A square root is a side length.

A square with area 25 has side √25 = 5.

side = √25 = 5
area = 25
= side × side
= 5 × 5

Watch the method

Squaring & its inverse

√25 = 5 because 5² = 25.

1 / 2
25\sqrt{25}
1

Ask the question

√25 asks: what number squared gives 25?

25=?\sqrt{25} = ?
2

Find the root

5² = 25, so √25 = 5.

25=5\sqrt{25} = 5
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.

Undo the square

For non-negative numbers, squaring and square-rooting are opposite operations. √(n²) = n and (√n)² = n.

Why it works

5 → square → 25 → root → 5.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

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

EX 2medium

Evaluate √25

1

Ask the question

√25 asks: what number squared gives 25? √25 = ?

2

Find the root

5² = 25, so √25 = 5. √25 = 5

EX 3hard

Evaluate √49

1

Ask the question

√49 asks: what number squared gives 49? √49 = ?

2

Find the root

7² = 49, so √49 = 7. √49 = 7

04 / COMMON TRAPS

Where students slip.

Trap

Thinking √25 = 12.5 (dividing by 2).

Fix

A root is not halving; √25 = 5 because 5·5 = 25.

Trap

Forgetting which operation undoes squaring.

Fix

The square root reverses 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 √36

Need a hint?
  • Ask: what number times itself gives this?
  • Check by squaring your answer.
C2

Evaluate √64

Need a hint?
  • Ask: what number times itself gives this?
  • Check by squaring your answer.
C3

Evaluate √100

Need a hint?
  • Ask: what number times itself gives this?
  • Check by squaring your answer.
C4

Evaluate √100

Need a hint?
  • Ask: what number times itself gives this?
  • Check by squaring your answer.
Apply

Apply (4)

A1

Evaluate √121

Need a hint?
  • Ask: what number times itself gives this?
  • Check by squaring your answer.
A2

Evaluate √144

Need a hint?
  • Ask: what number times itself gives this?
  • Check by squaring your answer.
A3

Evaluate √81

Need a hint?
  • Ask: what number times itself gives this?
  • Check by squaring your answer.
A4

Evaluate √9

Need a hint?
  • Ask: what number times itself gives this?
  • Check by squaring your answer.
Extension

Extension (4)

E1

Evaluate √64

Need a hint?
  • Ask: what number times itself gives this?
  • Check by squaring your answer.
E2

Evaluate √81

Need a hint?
  • Ask: what number times itself gives this?
  • Check by squaring your answer.
E3

Evaluate √64

Need a hint?
  • Ask: what number times itself gives this?
  • Check by squaring your answer.
E4

Evaluate √100

Need a hint?
  • Ask: what number times itself gives this?
  • Check by squaring your answer.