Roots

Squared

Means multiplied by itself: a² = a × a.

Square root

The reverse process of squaring; what number multiplied by itself gives the original number.

What is the square root of 49?

7, because 7 × 7 = 49.

Square root of 29.16

5, as calculated using a calculator.

Positive square root of 36

6, because 6 × 6 = 36.

Negative square root of 36

-6, because -6 × -6 = 36.

Rule for multiplying square roots

The square root of a times the square root of a equals a (√a × √a = a).

Cubed

Means multiplied by itself and then again: a³ = a × a × a.

Cube root

The reverse process of cubing; what number multiplied by itself twice gives the original number.

What is the cube root of 27?

3, because 3 × 3 × 3 = 27.

Cube root of 4913

17, as calculated using a calculator.

Difference between square roots and square numbers

A square root is a number that gives the original number when multiplied by itself.

What is the square root of 196?

14, calculated without a calculator.

What is the cube root of 9261?

21.

Volume of a cube is 1.728cm³; find side length.

3.21 cm.

Cube root of 19.34 + (1.3 + 2.5)²

17.1242244213, as shown on a calculator.