How do you simplify $3 \sqrt{(27 + 1)}$ $3sqrt( (27 + 1 ))$ ?

Question

1518 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-11T21:59:20

See a solution process below:

First, rewrite the expression within the radical as:

$3 \sqrt{27 + 1} \Rightarrow 3 \sqrt{28} \Rightarrow 3 \sqrt{4 \cdot 7}$ $3sqrt(27 + 1) => 3sqrt(28) => 3sqrt(4 * 7)$

Now, use this rule for radicals to simplify the radical:

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

$3 \sqrt{4 \cdot 7} \Rightarrow$ $3sqrt(color(red)(4) * color(blue)(7)) =>$

$3 \sqrt{4} \cdot \sqrt{7} \Rightarrow$ $3sqrt(color(red)(4)) * sqrt(color(blue)(7)) =>$

$3 \cdot 2 \cdot \sqrt{7} \Rightarrow$ $3 * 2 * sqrt(color(blue)(7)) =>$

$6 \sqrt{7}$ $6sqrt(color(blue)(7))$

How do you simplify 3sqrt( (27 + 1 ))3√(27+1)3sqrt( (27 + 1 ))?