How do you simplify $4 \sqrt{48}$ $4sqrt48$ ?

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Answer 1 · 2018-03-06T23:43:28

See a solution process below:

First, rewrite the expression as:

$4 \sqrt{16 \cdot 3}$ $4sqrt(16 * 3)$

Then use this rule for exponents to simplify the radical:

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

$4 \sqrt{16 \cdot 3} \Rightarrow$ $4sqrt(color(red)(16) * color(blue)(3)) =>$

$4 \cdot \sqrt{16} \cdot \sqrt{3} \Rightarrow$ $4 * sqrt(color(red)(16)) * sqrt(color(blue)(3)) =>$

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

$16 \sqrt{3}$ $16sqrt(3)$

Answer 2 · 2018-03-06T23:47:35

$4 \sqrt{48} = 16 \sqrt{3}$ $4sqrt48=color(blue)(16sqrt3$

Simplify:

$4 \sqrt{48}$ $4sqrt48$

Prime factorize $48$ $48$ .

$4 \sqrt{2 \cdot 2 \cdot 2 \cdot 2 \cdot 3}$ $4sqrt(2*2*2*2*3)$

$4 \sqrt{2^{2} \cdot 2^{2} \cdot 3}$ $4sqrt(2^2*2^2*3)$

Apply rule: $\sqrt{x^{2}} = x$ $sqrt(x^2)=x$

$4 \cdot 2 \cdot 2 \sqrt{3}$ $4*2*2sqrt3$

Simplify.

$16 \sqrt{3}$ $16sqrt3$

How do you simplify 4sqrt484√48 4sqrt48?