Question

simplify the radical expression

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Answer 1

\[4\sqrt{6}+5\sqrt{6}\]

Answer 2

What is 4 oranges + 5 oranges = ?
What is 4x + 5x = ?

Answer 3

Simplify 4√6 + 5√6

Simplify 4√6.

Checking square roots, we see that 22 = 4 and 32 = 9.
Our answer is not an integer, so we try simplify it into the product of an integer and a radical.

We do this by listing each product combo of 6 checking for integer square root values below:
√6 = √1√6
√6 = √2√3

From that list, the highest factor that has an integer square root is 1.
Therefore, we use the product combo √6 = √1√6
Evaluating square roots, we see that √1 = 1

Since 1 is the greatest common factor, this square root cannot be simplified any further:
Multiply by our constant of 4
4√6 = 4√6

Simplify 5√6.

Checking square roots, we see that 22 = 4 and 32 = 9.
Our answer is not an integer, so we try simplify it into the product of an integer and a radical.

We do this by listing each product combo of 6 checking for integer square root values below:
√6 = √1√6
√6 = √2√3

From that list, the highest factor that has an integer square root is 1.
Therefore, we use the product combo √6 = √1√6
Evaluating square roots, we see that √1 = 1

Since 1 is the greatest common factor, this square root cannot be simplified any further:
Multiply by our constant of 5
5√6 = 5√6

Simplifying the original expression, we get:
Group √6 terms → 4√6 + 5√6 = 9√6

Build our final simplified answer:
9√6

Calculators are always great ways to check your work! This is a great resource:

http://www.wolframalpha.com/input/?i=simplifying+radical+expressions&f1=4sqrt%286%29%2B5sqrt%286%29&f=RadicalSimplifierCalculator.radical_4sqrt%286%29%2B5sqrt%286%29

Good luck! =)