Question
Simplify by factoring. Assume that all variables represent nonnegative numbers. \( \sqrt{50 t^{2}} \) The answer is \( \square \). (Type an exact answer, using radicals as needed.)
Ask by Griffin Goodwin. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified form is \( 5\sqrt{2}t \).
Solution
Calculate or simplify the expression \( \sqrt{50t^2} \).
Simplify the expression by following steps:
- step0: Solution:
\(\sqrt{50t^{2}}\)
- step1: Write as a product:
\(\sqrt{25\times 2t^{2}}\)
- step2: Write in exponential form:
\(\sqrt{5^{2}\times 2t^{2}}\)
- step3: Reorder the terms:
\(\sqrt{5^{2}t^{2}\times 2}\)
- step4: Use the properties of radicals:
\(\sqrt{5^{2}t^{2}}\times \sqrt{2}\)
- step5: Simplify the root:
\(5\sqrt{2}\times t\)
The simplified form of \( \sqrt{50t^2} \) is \( 5\sqrt{2}t \).
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Simplify this solution Mind Expander
To simplify \( \sqrt{50 t^{2}} \), we can break it down into its prime factors: \( 50 = 25 \times 2 \) and \( t^{2} \) is a perfect square. Therefore, we rewrite the expression as: \[ \sqrt{50 t^{2}} = \sqrt{25 \times 2 \times t^{2}} = \sqrt{25} \cdot \sqrt{2} \cdot \sqrt{t^{2}} \] Since \( \sqrt{25} = 5 \) and \( \sqrt{t^{2}} = t \), we can combine these: \[ = 5t\sqrt{2} \] So, the simplified form is \( 5t\sqrt{2} \).
