Simplifying Radicals With Negative Radicands and Powers of i

Front

What is a radical?

Back

A radical is a symbol that represents the root of a number, typically the square root, cube root, etc.

Front

What does it mean to simplify a radical?

Back

To simplify a radical means to express it in its simplest form, removing any perfect squares or higher powers from under the radical sign.

Front

What is the square root of 75?

Back

5√3

Front

How do you simplify the square root of a negative number?

Back

To simplify the square root of a negative number, factor out -1 and use 'i' (the imaginary unit) to express it.

Front

What is the simplified form of √-28?

Back

2i√7

Front

What is the value of i^2?

Back

-1

Front

What is the value of i^4?

Back

1

Front

What is the definition of the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1.

Front

What is the simplified form of √-23?

Back

i√23

Front

How do you express i raised to a power?

Back

To express i raised to a power, reduce the exponent modulo 4, since i^4 = 1.