Question

simplify:
\sqrt{5a\sqrt{6^8}} = \square simplify and remove all perfect squares from inside the square root.
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question 10
simplify: \sqrt{507w^{10}z^{13}}
\bigcirc 13w^{5}z^{6}\sqrt{3z}
\bigcirc w^5z^6\sqrt{507z}
\bigcirc w^{10}z^{13}\sqrt{507z}
\bigcirc 13w^5z^6\sqrt{3z}

Explanation:

First Problem: $\sqrt[3]{64a^9b^{12}}$

Step1: Factor into perfect cubes

$\sqrt[3]{64a^9b^{12}} = \sqrt[3]{4^3 \cdot (a^3)^3 \cdot (b^4)^3}$

Step2: Extract perfect cubes

$\sqrt[3]{4^3} \cdot \sqrt[3]{(a^3)^3} \cdot \sqrt[3]{(b^4)^3} = 4a^3b^4$

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Second Problem: $\sqrt{507w^{10}z^{13}}$

Step1: Factor into perfect squares

$\sqrt{507w^{10}z^{13}} = \sqrt{169 \cdot 3 \cdot (w^5)^2 \cdot (z^6)^2 \cdot z}$

Step2: Extract perfect squares

$\sqrt{13^2} \cdot \sqrt{(w^5)^2} \cdot \sqrt{(z^6)^2} \cdot \sqrt{3z} = 13w^5z^6\sqrt{3z}$

Answer:

$4a^3b^4$