Question
Simplify. \( \sqrt{125}+\sqrt{28}-8 \sqrt{5} \) \( [?] \sqrt{\square}-\square \sqrt{\square} \)
Ask by French Mullins. in the United States
Mar 06,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The value of \( \sqrt{\square}-\square \sqrt{\square} \) is \( -3\sqrt{5}+2\sqrt{7} \), so \( \square = 5 \) and \( \square = 7 \).
Solution
Calculate or simplify the expression \( \sqrt{125}+\sqrt{28}-8\sqrt{5} \).
Calculate the value by following steps:
- step0: Calculate:
\(\sqrt{125}+\sqrt{28}-8\sqrt{5}\)
- step1: Simplify the root:
\(5\sqrt{5}+\sqrt{28}-8\sqrt{5}\)
- step2: Simplify the root:
\(5\sqrt{5}+2\sqrt{7}-8\sqrt{5}\)
- step3: Subtract the numbers:
\(-3\sqrt{5}+2\sqrt{7}\)
The simplified expression is \( -3\sqrt{5}+2\sqrt{7} \).
Now, we need to find the value of \( \sqrt{\square}-\square \sqrt{\square} \) that is equal to \( -3\sqrt{5}+2\sqrt{7} \).
Simplify the expression by following steps:
- step0: Solution:
\(\sqrt{\square }-\square \sqrt{\square }\)
The expression \( \sqrt{\square}-\square \sqrt{\square} \) is equal to \( -3\sqrt{5}+2\sqrt{7} \).
Therefore, the value of \( \square \) is 5 and \( \square \) is 7.
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Simplify this solution Beyond the Answer
To simplify the expression \( \sqrt{125}+\sqrt{28}-8 \sqrt{5} \), we first break down the square roots: 1. \( \sqrt{125} = \sqrt{25 \cdot 5} = 5 \sqrt{5} \) 2. \( \sqrt{28} = \sqrt{4 \cdot 7} = 2 \sqrt{7} \) Now we can rewrite the expression: \[ 5\sqrt{5} + 2\sqrt{7} - 8\sqrt{5} = (5\sqrt{5} - 8\sqrt{5}) + 2\sqrt{7} \] Combine the like terms: \[ -3\sqrt{5} + 2\sqrt{7} \] Now we arrange it in the desired format: \[ 2\sqrt{7} - 3\sqrt{5} \] Thus, the final simplified expression is: \(\sqrt{28}-3\sqrt{5}\)
