sqrt(80) sqrt(45) ·

02 May 2024, 00:00

Enter radical expression

Simplify √80√45

Simplify √80.

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

List each product combo of 80
checking for integer square root values below:
√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

Simplify our product

√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:

√80√45

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.
Simplify it into the product of an integer and a radical.

List each product combo of 8045
checking for integer square root values below:
√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 = √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

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radicalThe √ symbol that is used to denote square root or nth roots
√radical expressionsan nth root of a number x is a number r which, when raised to the power n, yields x
n√xsquare roota factor of a number that, when multiplied by itself, gives the original number
√x

sqrt(80) sqrt(45)

Simplify 80. Checking square roots, we see that 82 = 64 and 92 = 81.Our answer is not an integer.Simplify it into the product of an integer and a radical. List each product combo of 80checking for integer square root values below:80 = 18080 = 24080 = 42080 = 51680 = 810