2sqrt(28)%2b3sqrt(63)-sqrt(49)

Publish date: 2024-03-29
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Enter radical expression

Simplify 2√28%2b3√63 - √49

Simplify 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)√7
2√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√7
Group Constants → -7
Build our final simplified answer:
4√7 - 7
Evaluate the product of the 1 square root terms:
2√28%2b3√63-√49
Multiply the product of the outside constants:
2 = 2
The square root of products is equal to the product of square roots:
Product of the inner constants under the radical sign = 28 = 28
List out the product of all variables and exponents:
b3631 = b3631
Our final product term is 2√28b363, 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√7

Therefore, 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√7b363
Our final answer is the factored out piece and the expression under the radical
2√7b363
Multiply by outside constant of 2 to get our final answer:
2 x 2√7b363 = 4√7b363

What is the Answer?

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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

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