Undo the square

The idea

If y = x², then x is a square root of y; taking the square root is the inverse operation of squaring.

A square tablecloth

A square tablecloth has an area of 49 sq cm.

How long is one side?

• 7 cm
• 24.5 cm
• 14 cm

Find the side

Drag the orange corner (or use − and +) until the area matches. The side you find is the square root of the area.

Going backwards

If y = x², then x is a square root of y. Taking the square root is the inverse (the undo) of squaring.

The side of a square with area 49 is 7, so 7 is the square root of 49.

• x | Square it: x² | Square root: back to x
• 3 | 9 | 3
• 7 | 49 | 7
• 12 | 144 | 12

Notes

If y = x², then x is a square root of y. Taking the square root is the inverse operation of squaring.

Check yourself

A square has an area of 81 sq cm. How long is its side?

Answer: 9 cm

9 × 9 = 81, so the side is 9 cm. 9 is the square root of 81.

Which number is a square root of 144?

Start with 15. Square it, then take the square root of the answer. What do you get?

Answer: 15

15² = 225 and the square root of 225 is 15. The square root undoes the squaring.

• 12 — correct. Yes! 12 × 12 = 144.
• 72. 72 is half of 144. A square root times itself gives 144: 72 × 72 is much bigger.
• 24. 24 × 24 = 576, not 144.
• 14.4. 14.4 is 144 ÷ 10. We need a number that multiplied by itself gives 144.