Math

QuestionSimplify the expression: 8+2\sqrt{8}+\sqrt{2}.

Studdy Solution

STEP 1

Assumptions1. We are working with real numbers. We are using the standard rules of arithmetic and algebra

STEP 2

First, we need to simplify the square root of8. We can do this by finding the prime factorization of8 and then simplifying the square root.
\sqrt{8} = \sqrt{2^}

STEP 3

Now, we can simplify the square root of 232^3 by using the rule ab=ab/2\sqrt{a^b} = a^{b/2}.
23=23/2\sqrt{2^3} =2^{3/2}

STEP 4

We can further simplify 23/22^{3/2} by separating it into 21/2212^{1/2} *2^{1}.
23/2=21/221=222^{3/2} =2^{1/2} *2^{1} =2\sqrt{2}

STEP 5

Now that we have simplified 8\sqrt{8} to 222\sqrt{2}, we can substitute this back into the original equation.
22+22\sqrt{2} + \sqrt{2}

STEP 6

We can simplify this further by combining like terms.
22+2=322\sqrt{2} + \sqrt{2} =3\sqrt{2}So, 8+2=32\sqrt{8}+\sqrt{2} =3\sqrt{2}.

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