Square root of 2(5 + square root of 8) is irrational and equal to what


We are given with two factors: square root of 2 and 5 + square root of 8. We use a scientific calculator that displays irrational answers. The product of the two factors is 4 + 5 square root of 2. The answer is irrational since the square root sign in the answer is present.
Sqrt2(5+sqrt8) = 5sqrt2 +sqrt16 = 4+5sqrt2 so result that choice D. is right sure 

Answer D

The answer is Yes

Step-by-step explanation:

The answer is Irrational Number.

Step-by-step explanation:

In order to determine the group of numbers, we have to use the properties of root.

The number is:

\sqrt{2} *(5+\sqrt{8})\\(\sqrt{2}*5)+(\sqrt{2}*\sqrt{8})\\5*\sqrt{2} +\sqrt{16}\\5*\sqrt{2} +4

Then, we have to know three definitions:

All rational numbers can be written as fractions equation, with a being an integer and b being a natural number. Irrational numbers can not be written as fractions notation.When a prime number is inside of a square root, the number is always a irrational.

Finally, 5*\sqrt{2} +4 has a \sqrt{2}, that it is a irrational number, therefore the addition is a irrational number too.

For this case we have the following product:


Applying the distributive property we have:


Then, rewriting the expression we have:



We note that the answer is a irrational number, because the square root of two is not an exact number.


It is irrational and equal to 4 + 5square root of 2.

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