QuestionCalculate $(5 \odot 45) \odot 60$ where $x \odot y=\sqrt{x y}$ for positive $x$ and $y$ .

Studdy Solution

STEP 1

Assumptions1. The operation $\odot$ is defined as $x \odot y=\sqrt{x y}$ for all positive numbers $x$ and $y$ . . We need to find the value of $(5 \odot45) \odot60$ .

STEP 2

First, we need to calculate the value of $5 \odot45$ . According to the definition of the operation $\odot$ , this is equal to $\sqrt{5 \times45}$ .
$5 \odot45 = \sqrt{5 \times45}$

STEP 3

Now, calculate the value of $5 \odot45$ .
$5 \odot45 = \sqrt{5 \times45} = \sqrt{225} =15$

STEP 4

Now that we have the value of $\odot45$ , we can substitute this into the original expression to find the value of $( \odot45) \odot60$ .
$( \odot45) \odot60 =15 \odot60 = \sqrt{15 \times60}$

STEP 5

Finally, calculate the value of $(5 \odot45) \odot60$ .
$(5 \odot45) \odot60 = \sqrt{15 \times60} = \sqrt{900} =30$ So, $(5 \odot45) \odot60 =30$ .

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