Comparing a Radical to an Integer

Comparing a Radical to an Integer

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

Definition

(sqrt(1))^2 = 1^2 = 1 (sqrt(2))^2 = (1.414...)^2 = 2 (sqrt(3))^2 = (1.732...)^2 = 3 (sqrt(4))^2 = 2^2 = 4

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

Determine which is the greater number. 8, sqrt(56)

Square both sides.
Then 64 > 56.

So 8 > √56.

Example 2

Determine which is the greater number. -sqrt(29), -6

Leave the (-) sign and square both sides.
Then -29 > -36.

So -√29 > -6.