Powers & Roots (Edexcel IGCSE Maths A (Modular))

A square root of a number is a value that, when squared, gives the original number.

E.g. 3 is the square root of 9 because 3² = 3 x 3 = 9.

True.

Every positive number has two square roots, one positive and one negative.

E.g. and

False.

The cube root of a negative number will also be a negative number.

For example, -5 is a cube root of -125.

The reciprocal of a number is the number that you multiply it by to get 1.

For example, is the reciprocal of .

You can estimate the root of a number by finding the closest integer roots either side of it.

E.g. To find

and

So is between and

Any non-zero number raised to the power of 0 is equal to 1.

E.g. 2⁰ = 1.

False.

Any number raised to the power 1 is just itself.

E.g. .

If you raise a non-zero number to the power of -1 you get the reciprocal of the number.

E.g. .

If you raise a non-zero number to the power of ½ you get its positive square root.

E.g. .

If you multiply two powers with the same base number, you add the indices together.