Square Roots · Evaluate & estimate · 2.2

Bigger perfect squares.

The same idea extends past 100: √144 = 12, √169 = 13, √196 = 14, √225 = 15. Knowing the squares of 11–15 covers most school problems.

01 / THE IDEA

See it work.

Watch the method

Bigger perfect squares

√169 = 13 because 13² = 169.

1 / 1
169\sqrt{169}
1

Recognise the perfect square

169 = 13², so √169 = 13.

169=13\sqrt{169} = 13
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.

Up to 15

11² = 121, 12² = 144, 13² = 169, 14² = 196, 15² = 225. Learn these and big roots become easy.

Why it works

√225 = 15.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Evaluate √256

1

Ask the question

√256 asks: what number squared gives 256? √256 = ?

2

Find the root

16² = 256, so √256 = 16. √256 = 16

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 √196

1

Ask the question

√196 asks: what number squared gives 196? √196 = ?

2

Find the root

14² = 196, so √196 = 14. √196 = 14

04 / COMMON TRAPS

Where students slip.

Trap

Stopping the table at 12.

Fix

Extend it to 15 for bigger roots.

Trap

Estimating when it is exact.

Fix

These are perfect squares — give the exact 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 √225

Need a hint?
  • Recall the squares of 11–15.
  • Check by squaring.
C2

Evaluate √289

Need a hint?
  • Recall the squares of 11–15.
  • Check by squaring.
C3

Evaluate √196

Need a hint?
  • Recall the squares of 11–15.
  • Check by squaring.
C4

Evaluate √225

Need a hint?
  • Recall the squares of 11–15.
  • Check by squaring.
Apply

Apply (4)

A1

Evaluate √169

Need a hint?
  • Recall the squares of 11–15.
  • Check by squaring.
A2

Evaluate √196

Need a hint?
  • Recall the squares of 11–15.
  • Check by squaring.
A3

Evaluate √225

Need a hint?
  • Recall the squares of 11–15.
  • Check by squaring.
A4

Evaluate √169

Need a hint?
  • Recall the squares of 11–15.
  • Check by squaring.
Extension

Extension (4)

E1

Evaluate √289

Need a hint?
  • Recall the squares of 11–15.
  • Check by squaring.
E2

Evaluate √196

Need a hint?
  • Recall the squares of 11–15.
  • Check by squaring.
E3

Evaluate √144

Need a hint?
  • Recall the squares of 11–15.
  • Check by squaring.
E4

Evaluate √256

Need a hint?
  • Recall the squares of 11–15.
  • Check by squaring.