2sqrt(28)%2520%252b%25203sqrt(63)%2520-%2520sqrt(49)
%252520%25252b%2525203sqrt(63)%252520-%252520sqrt(49)&pl=Simplify+Radical+Expression)
Enter radical expression
Simplify 2√28%2520%252b%25203√63%2520 - %2520√49Simplify 2√28.
Checking square roots, we see that 52 = 25 and 62 = 36.
Our answer is not an integer.
Simplify it into the product of an integer and a radical.
List each product combo of 28
checking for integer square root values below:
√28 = √1√28
√28 = √2√14
√28 = √4√7
From that list, the highest factor that has an integer square root is 4.
Therefore, we use the product combo √28 = √4√7
Evaluating square roots, we see that √4 = 2
Simplify our product
Multiply by our constant of 2
2√28 = (2 x 2)√72√28 = 4√7
Simplify √49.
If you use a guess and check method, you see that 62 = 36 and 82 = 64.
Since 36 < 49 < 64 the next logical step would be checking 72.
72 = 7 x 7
72 = 49 <--- We match our original number!!!
Therefore, √49 = ±7
Simplifying the original expression, we get:
Group √7 terms → 4√7 = 4√7Group Constants → -7
Build our final simplified answer:
4√7 - 7Evaluate the product of the 1 square root terms:
2√28%2520%252b%25203√63%2520-%2520√49Multiply the product of the outside constants:
2 = 2The square root of products is equal to the product of square roots:
Product of the inner constants under the radical sign = 28 = 28List out the product of all variables and exponents:
b1 = b1Our final product term is 2√28b, simplify it
Simplify √28.
Checking square roots, we see that 52 = 25 and 62 = 36.
Our answer is not an integer.
Simplify it into the product of an integer and a radical.
List each product combo of 28
checking for integer square root values below:
√28 = √1√28
√28 = √2√14
√28 = √4√7
From that list, the highest factor that has an integer square root is 4.
Therefore, we use the product combo √28 = √4√7
Evaluating square roots, we see that √4 = 2
Simplify our product
√28 = 2√7Therefore, we can factor out 2 from the radical, and leave 7 under the radical
We can factor out the following portion using the highest even powers of variables:
√ = =Our leftover piece under the radical becomes 2√7b
Our final answer is the factored out piece and the expression under the radical
2√7b
Multiply by outside constant of 2 to get our final answer:
2 x 2√7b = 4√7bWhat 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
Example calculations for the Radical Expressions Calculator
PlayTags:
Add This Calculator To Your Website
ncG1vNJzZmivp6x7rq3ToZqepJWXv6rA2GeaqKVfp66lsddnp6Gob6PCromRrKirrFhnhWpxkW5pbmpgWn92fpRrmV5qZWeCc3ySrKirrFhrgGpxkW5pbmpgYnJzgZFuaWmroafBaYCYYl2ppG2Itq68y6KdsmOClrGqr8ClYn6woKeytL%2FIqKU%3D