Simplify √80√45

Simplify √80.

Checking square roots, we see that 8

Our answer is not an integer, so we try simplify it into the product of an integer and a radical.

√80 = √1√80

√80 = √2√40

√80 = √4√20

√80 = √5√16

√80 = √8√10

From that list, the highest factor that has an integer square root is 16.

Therefore, we use the product combo √80 = √16√5

Evaluating square roots, we see that √16 = 4

√80 =

Group √5 terms → 4√5 = 4√5

√80√45

1 = 1

Product of the inner constants under the radical sign = 8045 = 8045

Our final product term is 1√8045, simplify it

Simplify √8045.

Checking square roots, we see that 89

Our answer is not an integer, so we try simplify it into the product of an integer and a radical.

√8045 = √1√8045

√8045 = √5√1609

From that list, the highest factor that has an integer square root is 1.

Therefore, we use the product combo √8045 = √1√8045

Evaluating square roots, we see that √1 = 1

Since 1 is the greatest common factor, this square root cannot be simplified any further:

This is also known as a surd

√8045 =

Therefore, we can factor out from the radical, and leave 8045 under the radical

√ = =

Our leftover piece under the radical becomes √8045

Our final answer is the factored out piece and the expression under the radical

1 x √8045 =