2sqrt12-3sqrt27

July 2024 · 3 minute read
12 - 3√27

Simplify 2√0.

If you use a guess and check method, you see that -12 = 1 and 12 = 1.
Since 1 < 0 < 1 the next logical step would be checking 02.

02 = 0 x 0
02 = 0 <--- We match our original number!!!
Multiplying by our outside constant, we get 2 x 0 = 0
Therefore, 2√0 = ±0

Simplify 3√27.

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 27
checking for integer square root values below:
√27 = √1√27
√27 = √3√9

From that list, the highest factor that has an integer square root is 9.
Therefore, we use the product combo √27 = √9√3
Evaluating square roots, we see that √9 = 3

Simplify our product
Multiply by our constant of 3
3√27 = (3 x 3)√3
3√27 = 9√3
Simplifying the original expression, we get:
Group Constants → 0
Group √3 terms → 9√3 = 9√3
Build our final simplified answer:
0 + 9√3
Evaluate the product of the 1 square root terms:
2√12-3√27
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 = 12 = 12
List out the product of all variables and exponents:
Our final product term is 2√12, simplify it

Simplify √12.

Checking square roots, we see that 32 = 9 and 42 = 16.
Our answer is not an integer.
Simplify it into the product of an integer and a radical.

List each product combo of 12
checking for integer square root values below:
√12 = √1√12
√12 = √2√6
√12 = √3√4

From that list, the highest factor that has an integer square root is 4.
Therefore, we use the product combo √12 = √4√3
Evaluating square roots, we see that √4 = 2

Simplify our product
√12 = 2√3

Therefore, we can factor out 2 from the radical, and leave 3 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√3
Our final answer is the factored out piece and the expression under the radical
2√3
Multiply by outside constant of 2 to get our final answer:
2 x 2√3 = 4√3

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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