# Comparing a Radical to an Integer

How to compare a radical to an integer: examples and their solutions.

## Definition

A radical is a number with a square root ( √ ).

√■ is a number that satisfy (√■ )^{2} = ■.

It's a way to express numbers.

For example:

√1 (= 1) is a number that satisfy (√1)^{2} = 1.

√2 (≈ 1.414...) is a number that satisfy (√2)^{2} = 2.

√3 (≈ 1.732...) is a number that satisfy (√3)^{2} = 3.

√4 (= 2) is a number that satisfy (√4)^{2} = 4.

So it's obvious that

the number inside the radical sign ( √ )

has to be (+).

## Example 1

Square both sides.

Then 64 > 56.

So 8 > √56.

## Example 2

Leave the (-) sign and square both sides.

Then -29 > -36.

So -√29 > -6.