KS1 (Age 5-7)KS2 (Age 7-11)11 Plus (Age 7-11)KS3 (Age 11-14)GCSE (Age 14-17)PSHE A.I.ESL Spanish Specialist Games

Need help with Level 5-6 Numbers - Roots? Ask our AI Tutor!

AI Tutor - Lucy

Connecting with Tutor...

Please wait while we establish connection

Hi! I'm Lucy, your AI tutor. How can I help you with Level 5-6 Numbers - Roots today?

now

How good are you at roots? That is, mathematical roots not tree roots!

Level 5-6 Numbers - Roots

Roots undo powers. Learn square roots to find side lengths, solve equations, and estimate values between perfect squares.

Explore the Topic →

(quiz starts below)

Fascinating Fact:

Architects use square roots to calculate diagonal lengths. A square floor 4 m wide has a diagonal of √(4² + 4²) = √32 ≈ 5.66 m.

In KS3 Maths, you will use roots to reverse powers and to solve practical problems. Square roots help find missing lengths, check solutions, and estimate values between perfect squares.

Key Terms

Square root: A number which, when multiplied by itself, gives the original number. For example, the square root of 25 is 5.
Perfect square: A whole number made by squaring another whole number, like 1, 4, 9, 16, 25.
Radical sign: The symbol √ used to show a root, as in √36 = 6.

Frequently Asked Questions (Click to see answers)

What is a square root in KS3 Maths?

A square root is a number that multiplies by itself to make another number. For example, 7×7 = 49, so the square root of 49 is 7.

How can I estimate a square root without a calculator?

Find the two nearest perfect squares and interpolate. For example, √50 is between √49 = 7 and √64 = 8, so it is a little more than 7.

What is the difference between squares and square roots?

Squaring multiplies a number by itself, like 6² = 36. A square root reverses this process, so √36 = 6.

Try These Related Quizzes

1 .

The square root of 425 lies between .......

19 and 20

20 and 21

21 and 22

23 and 24

20² = 400; 21² = 441. ?425 = 20.61552813.......

2 .

What is the square root of 5⁴?

125

250

To find the square root of a power number you divide the index by 2. ?(5⁴) = 5²

3 .

What is the square root of 64 x 144?

The square root of a product is the product of the square roots. ?64 x ?144 = 8 x 12

4 .

The cube root of 216 is .......

Since 16² = 256, 16³ must be bigger and 26³ or 36³ will be bigger still, so 6 is the only sensible answer

5 .

What is the total surface area of a cube which has a volume of 729 cm³?

54 cm²

81 cm²

360 cm²

486 cm²

?729 = 9 so each square face has an area of 81 cm². A cube has six square faces; 6 x 81 = 486

6 .

What is the cube root of 7⁹?

147

343

560

To find the cube root of a power number you divide the index by 3. ?(7⁹) = 7³

7 .

A cube of volume 1,000 cm³ has side length .......

1 cm

10 cm

100 cm

1 m

?1,000 = 10

8 .

The square with the same area as a rectangle measuring 9 cm by 16 cm has side length .......

6 cm

9 cm

12 cm

15 cm

9 x 16 = 144. ?144 = 12

9 .

A square of area 169 cm² has side length .......

43 cm

33 cm

23 cm

13 cm

?169 = 13

10 .

Which of these is not a way of writing the square root of 625?

5²

√125

625^1⁄₅

The square root of 125 is 11.18 to two decimal places.

You can find more about this topic by visiting BBC Bitesize - Roots

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)

**Unlimited Quizzes Await You! 🚀**

Hey there, quiz champ! 🌟 You've already tackled today's free questions.
Ready for more?

🔓 Unlock UNLIMITED Quizzes and challenge yourself every day. But that's
not all...

🔥 As a Subscriber you can join our thrilling "Daily Streak" against other
quizzers. Try to win a coveted spot on our Hall of Fame Page.

Don't miss out! Join us now and keep the fun rolling. 🎉

Subscribe & Play

**Unlimited Quizzes Await You! 🚀**

Hey there, quiz champ! 🌟 You've already tackled today's free questions. Ready for more?

🔓 Unlock UNLIMITED Quizzes and challenge yourself every day. But that's not all...

🔥 As a Subscriber you can join our thrilling "Daily Streak" against other quizzers. Try to win a coveted spot on our Hall of Fame Page.

Don't miss out! Join us now and keep the fun rolling. 🎉

Subscribe & Play

Contact Details

Education Quizzes

Heron's Way, Wragg Marsh
Spalding
Lincolnshire
PE12 6HH
England

Email

admin@educationquizzes.com

Customer Service

Home Page Parents Students Tutors Teachers
Colour Filters Safe AI
Your Account

Here To Help

About Us

Our Team Testimonials Parent Reviews Terms and Conditions Privacy Policy

Leave Feedback