Question #02059

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Question #02059

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Answer 1 · 2017-09-21T23:51:25

$3 \sqrt{2} = 4.24264068712$ $3sqrt(2) = 4.24264068712$

Explanation:

The number 18 can be written as $9 \cdot 2$ $9*2$ . Thus $\sqrt{18} = \sqrt{9 \cdot 2}$ $sqrt(18) = sqrt(9*2)$ .

$\sqrt{9 \cdot 2}$ $sqrt(9*2)$ can also be writted as $\sqrt{9} \cdot \sqrt{2}$ $sqrt(9) * sqrt(2)$ , and since $\sqrt{9} = 3$ $sqrt(9) = 3$ , $\sqrt{18} = 3 \cdot \sqrt{2} = 3 \sqrt{2}$ $sqrt(18) = 3*sqrt(2) = 3sqrt(2)$ .

Answer 2 · 2017-09-22T00:00:00

$3 \sqrt{2}$ $3sqrt(2)$

Explanation:

The square root of 18 is an irrational number so it is common to express this in the form $a \sqrt{b}$ $asqrt(b)$ . This is known as a simplified surd.

For $\sqrt{18}$ $sqrt(18)$ notice we can factor the number inside the radical ( this is properly called the radicand):

So $\sqrt{18} \Rightarrow \sqrt{2 \times 9}$ $sqrt(18) => sqrt( 2 xx 9)$

Since 9 is an exact square we can extract the root and put the root before the radical.

$3 \sqrt{2}$ $3sqrt(2)$

The root of 2 is irrational so we leave it.

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Question #02059

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