How do you multiply the radicals $5 \sqrt{2} \cdot 8 \sqrt{2}$ $5sqrt2 * 8sqrt2$ ?

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How do you multiply the radicals $5 \sqrt{2} \cdot 8 \sqrt{2}$ $5sqrt2 * 8sqrt2$ ?

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Answer 1 · 2015-03-22T17:37:58

Remember that multiplications can be reordered and regrouped as we like. So

$5 \sqrt{2} \cdot 8 \sqrt{2} = 5 \cdot 8 \cdot \sqrt{2} \cdot \sqrt{2} = 40 \cdot 2 = 80$ $5sqrt2*8sqrt2=5*8*sqrt2*sqrt2=40*2=80$

In case it is not clear $\sqrt{2} \cdot \sqrt{2} = 2$ $sqrt2*sqrt2 = 2$ because that's how square root is defined.
Alternatively: $\sqrt{2} \cdot \sqrt{2} = \sqrt{2 \cdot 2} = \sqrt{4} = 2$ $sqrt2*sqrt2=sqrt(2*2)=sqrt4=2$

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How do you multiply the radicals $5 \sqrt{2} \cdot 8 \sqrt{2}$ $5sqrt2 * 8sqrt2$ ?

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