80%2b9√45Simplify 7√45.
Checking square roots, we see that 62 = 36 and 72 = 49.
Our answer is not an integer.
Simplify it into the product of an integer and a radical.
List each product combo of 45
checking for integer square root values below:
√45 = √1√45
√45 = √3√15
√45 = √5√9
From that list, the highest factor that has an integer square root is 9.
Therefore, we use the product combo √45 = √9√5
Evaluating square roots, we see that √9 = 3
Simplify our product
Multiply by our constant of 7
7√45 = (7 x 3)√57√45 = 21√5
Simplifying the original expression, we get:
Group √5 terms → 21√5 = 21√5Build our final simplified answer:
21√5Evaluate the product of the 1 square root terms:
7√80%2b9√45Multiply the product of the outside constants:
7 = 7The square root of products is equal to the product of square roots:
Product of the inner constants under the radical sign = 80 = 80List out the product of all variables and exponents:
b9451 = b9451Our final product term is 7√80b945, simplify it
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√5Therefore, we can factor out 4 from the radical, and leave 5 under the radical
We can factor out the following portion using the highest even powers of variables:
√ = =Our leftover piece under the radical becomes 4√5b945
Our final answer is the factored out piece and the expression under the radical
4√5b945
Multiply by outside constant of 7 to get our final answer:
7 x 4√5b945 = 28√5b945What is the Answer?
How does the Radical Expressions Calculator work?
Free Radical Expressions Calculator - Evaluates and simplifies radical expressions. Simplifying radical expressions.
This calculator has 1 input.
What 4 formulas are used for the Radical Expressions Calculator?
List out all factor products for SFind the highest factor with an integer square root and multiply the square root by the other square root of the factor
For more math formulas, check out our Formula Dossier
What 3 concepts are covered in the Radical Expressions Calculator?
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
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