How do you simplify $\sqrt{\frac{32 a^{4}}{b^{2}}}$ $sqrt((32a^4)/b^2)$ ?

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How do you simplify $\sqrt{\frac{32 a^{4}}{b^{2}}}$ $sqrt((32a^4)/b^2)$ ?

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Answer 1 · 2017-05-08T13:38:40

See the solution process below:

Explanation:

We can rewrite this expression as:

$\sqrt{\frac{(16 \cdot 2) a^{4}}{b^{2}}} \Rightarrow \sqrt{\frac{16 a^{4}}{b^{2}} \cdot 2}$ $sqrt(((16 * 2)a^4)/b^2) => sqrt((16a^4)/b^2 * 2)$

Using this rule for radicals we can further rewrite this expression as:

$\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$ $sqrt(a * b) = sqrt(a) * sqrt(b)$

$\sqrt{\frac{16 a^{4}}{b^{2}} \cdot 2} \Rightarrow \sqrt{\frac{16 a^{4}}{b^{2}}} \cdot \sqrt{2}$ $sqrt((16a^4)/b^2 * 2) => sqrt((16a^4)/b^2) * sqrt(2)$

We can now take the square root of the left radical to simplify this expression as:

$\frac{\pm 4 a^{2}}{b} \sqrt{2}$ $(+-4a^2)/bsqrt(2)$

Or, because the original question is given with only the principal root indicated:

$\frac{4 a^{2}}{b} \sqrt{2}$ $(4a^2)/bsqrt(2)$

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How do you simplify $\sqrt{\frac{32 a^{4}}{b^{2}}}$ $sqrt((32a^4)/b^2)$ ?

1 Answer

Explanation:

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How do you simplify $\sqrt{\frac{32 a^{4}}{b^{2}}}$ $sqrt((32a^4)/b^2)$ ?