How do you simplify $6 \sqrt{343} - 2 \sqrt{7}$ $6sqrt343 - 2 sqrt7$ ?

Question

1513 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-16T12:22:48

See a solution process below:

First, rewrite the radical on the left as:

$6 \sqrt{49 \cdot 7} - 2 \sqrt{7}$ $6sqrt(49 * 7) - 2sqrt(7)$

Next, use this rule for radicals to simplify the term on the left:

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

$6 \sqrt{49 \cdot 7} - 2 \sqrt{7} \Rightarrow$ $6sqrt(color(red)(49) * color(blue)(7)) - 2sqrt(7) =>$

$6 \sqrt{49} \sqrt{7} - 2 \sqrt{7} \Rightarrow$ $6sqrt(color(red)(49))sqrt(color(blue)(7)) - 2sqrt(7) =>$

$(6 \cdot 7 \sqrt{7}) - 2 \sqrt{7} \Rightarrow$ $(6 * 7sqrt(color(blue)(7))) - 2sqrt(7) =>$

$42 \sqrt{7} - 2 \sqrt{7}$ $42sqrt(color(blue)(7)) - 2sqrt(7)$

Now, factor out the common term to complete the simplification:

$(42 - 2) \sqrt{7} \Rightarrow$ $(42 - 2)sqrt(7) =>$

$40 \sqrt{7}$ $40sqrt(7)$

How do you simplify 6sqrt343 - 2 sqrt76√343−2√76sqrt343 - 2 sqrt7?