How do you evaluate 3√12 +4√18?

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How do you evaluate 3√12 +4√18?

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Answer 1 · 2018-04-07T05:21:46

$6 \sqrt{3} + 12 \sqrt{2}$ $6sqrt(3) + 12sqrt(2)$

Explanation:

The only way to simplify radicals is to take the radicand (the number under the radical) and split it into two factors, where one of them has to be a $perfect square$ $"perfect square"$

A $perfect square$ $"perfect square"$ is a product of two of the same numbers

Example: $9$ $9$ is a $perfect square$ $"perfect square"$ because $3 \cdot 3 = 9$ $3*3=9$

So, let's simplify and pull some numbers out of these radicals:

$3 \sqrt{12} + 4 \sqrt{18}$ $3sqrt(12) + 4sqrt(18)$ $Let's start with the left side$ $color(blue)(" Let's start with the left side"$
$3 \sqrt{4 \cdot 3} + 4 \sqrt{18}$ $3sqrt(4*3) + 4sqrt(18)$ $4 is a perfect square$ $color(blue)(" 4 is a perfect square")$
$3 \cdot 2 \sqrt{3} + 4 \sqrt{18}$ $3*2sqrt(3) + 4sqrt(18)$ $4 is a perfect square, so take a 2 out$ $color(blue)(" 4 is a perfect square, so take a 2 out")$
$6 \sqrt{3} + 4 \sqrt{18}$ $6sqrt(3) + 4sqrt(18)$ $Simplify: 3 \cdot 2 = 6, and leave the 3$ $color(blue)(" Simplify: "3*2=6," and leave the 3")$
$6 \sqrt{3} + 4 \sqrt{9 \cdot 2}$ $6sqrt(3) + 4sqrt(9*2)$ $9 is a perfect square$ $color(blue)(" 9 is a perfect square")$
$6 \sqrt{3} + 4 \cdot 3 \sqrt{2}$ $6sqrt(3) + 4*3sqrt(2)$ $9 is a perfect square, so take a 3 out$ $color(blue)(" 9 is a perfect square, so take a 3 out")$
$6 \sqrt{3} + 12 \sqrt{2}$ $6sqrt(3) + 12sqrt(2)$ $Simplify: 4 \cdot 3 = 12, and leave the 2$ $color(blue)(" Simplify: "4*3=12," and leave the 2")$
$6 \sqrt{3} + 12 \sqrt{2}$ $color(red)(6sqrt(3) + 12sqrt(2))$

Since $\sqrt{3}$ $sqrt(3)$ and $\sqrt{2}$ $sqrt(2)$ are different radicals, we can't add them, so we're done.

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How do you evaluate 3√12 +4√18?

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