Is sqrt(18)=3sqrt(2) ?

The answer to whether sqrt(18)=3sqrt(2) is True

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prove sqrt(18)=3sqrt(2)

prove

18 = 32

True

Solution steps

18 = 32

Manipulating left side

18

Simplify

18 : 32

18

Prime factorization of

18 : 2 \cdot 3^{2}

18

18

divides by

218 = 9 \cdot 2

= 2 \cdot 9

9

divides by

39 = 3 \cdot 3

= 2 \cdot 3 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3 \cdot 3

= 2 \cdot 3^{2}

= 3^{2} \cdot 2

Apply radical rule:

= 2 3^{2}

Apply radical rule:

3^{2} = 3

= 32

= 32

We showed that the two sides could take the same form

\Rightarrow True

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