QuestionSimplify $\sqrt{64 x^{2}}$ for $x>0$ .

Studdy Solution

STEP 1

Assumptions1. $x$ is a real number and $x >0$ . We are asked to simplify $\sqrt{64 x^{}}$

STEP 2

We can rewrite the expression under the square root as a product of two squares.
$\sqrt{64 x^{2}} = \sqrt{(8^{2} \cdot (x^{2})}$

STEP 3

The square root of a product can be written as the product of the square roots if all quantities under the square root are non-negative. $\sqrt{(8^{2} \cdot (x^{2})} = \sqrt{8^{2}} \cdot \sqrt{x^{2}}$

STEP 4

Calculate the square root of $8^{2}$ and $x^{2}$ .
$\sqrt{8^{2}} \cdot \sqrt{x^{2}} =8x$ So, the simplified form of $\sqrt{64 x^{2}}$ is $8x$ .

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