sqrt(80) sqrt(45)

<-- Enter expression (use sqrt for square root)

Simplify √8045

Simplify √80.

Checking square roots, we see that 82 = 64 and 92 = 81.
Our answer is not an integer, so we try simplify it into the product of an integer and a radical.

We do this by listing each product combo of 80 checking for integer square root values below:
80 = √180
80 = √240
80 = √420
80 = √516
80 = √810

From that list, the highest factor that has an integer square root is 16.
Therefore, we use the product combo √80 = √165
Evaluating square roots, we see that √16 = 4

Simplifying our product of radicals, we get our answer:
80 = 4√5

Simplifying the original expression, we get:
Group √5 terms → 4√5 = 4√5

Build our final simplified answer:
4√5

Evaluate the product of the 1 square root terms:
8045
Multiply the product of the outside constants:
1 = 1

The square root of products is equal to the product of square roots:
Product of the inner constants under the radical sign = 8045 = 8045

List out the product of all variables and exponents:
Our final product term is 1√8045, simplify it

Simplify √8045.

Checking square roots, we see that 892 = 7921 and 902 = 8100.
Our answer is not an integer, so we try simplify it into the product of an integer and a radical.

We do this by listing each product combo of 8045 checking for integer square root values below:
8045 = √18045
8045 = √51609

From that list, the highest factor that has an integer square root is 1.
Therefore, we use the product combo √8045 = √18045
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 = 8045

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

We can factor out the following portion using the highest even powers of variables:
= =
Our leftover piece under the radical becomes √8045
Our final answer is the factored out piece and the expression under the radical
8045

Multiply by outside constant of 1 to get our final answer:
1 x √8045 = 8045