radical 128 simplified
Understand the Problem
The question is asking for the simplified form of the expression 'radical 128', which refers to the square root of 128. The objective is to simplify this expression using the properties of square roots.
Answer
$8\sqrt{2}$
Answer for screen readers
The simplified form of $\sqrt{128}$ is $8\sqrt{2}$.
Steps to Solve
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Identify the expression We need to simplify the expression $\sqrt{128}$.
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Factor the number under the square root First, let's factor 128 into its prime factors. $$ 128 = 2^7 $$
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Use the properties of square roots According to the property of square roots, $\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$, we can express this as: $$ \sqrt{128} = \sqrt{2^7} = \sqrt{(2^6) \cdot 2} $$
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Simplify the square root Now, we can simplify this expression further: $$ \sqrt{(2^6) \cdot 2} = \sqrt{2^6} \cdot \sqrt{2} = 2^{6/2} \cdot \sqrt{2} = 2^3 \cdot \sqrt{2} $$
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Final simplification Calculating the power of 2 gives us: $$ 2^3 = 8 $$
Thus: $$ \sqrt{128} = 8\sqrt{2} $$
The simplified form of $\sqrt{128}$ is $8\sqrt{2}$.
More Information
The square root of 128 simplifies to $8\sqrt{2}$ since 128 can be expressed as $2^7$. This simplification is useful in various mathematical applications involving radicals.
Tips
- Forgetting to simplify after factoring the number under the square root.
- Not recognizing that $2^6$ can be pulled out of the square root as a whole number.
