To complete the expression involving radicals, we need to understand the elements presented:
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The first term is represented by a variable or number followed by a "and". Let's denote the first radicand that needs to be filled in.
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The second part "5(radicand) = 3" implies we have a square root expression where \(5\sqrt{\text{something}} = 3\). Let's solve for that something (the radicand):
\[ 5\sqrt{a} = 3 \implies \sqrt{a} = \frac{3}{5} \implies a = \left(\frac{3}{5}\right)^2 = \frac{9}{25} \]
So, the first radicand is \(\frac{9}{25}\).
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Now, moving on to "3 and (45, radicand) = 13". This means we have a second radical equation that we need to solve:
\(3 + \sqrt{b} = 13\).
Solving for \(b\):
\[ \sqrt{b} = 13 - 3 = 10 \implies b = 10^2 = 100 \]
Therefore, the radicand here is 100.
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Finally, let's look at the last part: "and __(radicand)". There’s no clear context or value given for this part, so this might just be a placeholder based on previous findings or values needed.
Putting it together, we summarize our findings:
- First Radicand: \(\frac{9}{25}\)
- Second Radicand: \(100\)
- Final Radicand needs specification but could utilize pattern or previous findings.
So a potential answer filling in the blanks might be:
Value 1: \(\sqrt{\frac{9}{25}}\), Value 2: \(5\sqrt{45}\) (or simply, \(10\)), and Final Radicand: is undetermined without further conditions.
Could you clarify what the last expression should represent, or do you want any specific radical values in the final filling?
1 answer