Math

QuestionSimplify 100x18\sqrt{100 x^{18}} for x>0x>0.

Studdy Solution

STEP 1

Assumptions1. The given expression is 100x18\sqrt{100 x^{18}} . The variable xx is greater than0

STEP 2

We can simplify the expression under the square root by separating it into two parts the constant and the variable.
100x18=100x18\sqrt{100 x^{18}} = \sqrt{100} \cdot \sqrt{x^{18}}

STEP 3

Now, simplify the square root of the constant100.
100=10\sqrt{100} =10So, the expression becomes10x1810 \cdot \sqrt{x^{18}}

STEP 4

Next, simplify the square root of the variable x18x^{18}.
Since x18x^{18} can be written as (x9)2(x^9)^2, the square root of x18x^{18} is x9x^9.
So, the expression becomes10x910 \cdot x^9

STEP 5

The simplified form of the given expression 100x18\sqrt{100 x^{18}} is 10x910x^9.

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