What is sqrt(9+2\sqrt{18)} ?

The solution to sqrt(9+2\sqrt{18)} is sqrt(6)+sqrt(3)

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simplify sqrt(9+2\sqrt{18)}

simplify

9 + 218

6 + 3

Decimal Notation

4.18154 \dots

Solution steps

9 + 218

218 = 62

= 9 + 62

= 6 + 62 + 3

= 3 \cdot 2 + 62 + 3

= (3)^{2} (2)^{2} + 62 + (3)^{2}

2323 = 62

= (32)^{2} + 2323 + (3)^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(32)^{2} + 2323 + (3)^{2} = (32 + 3)^{2}

= (32 + 3)^{2}

Apply radical rule:

(32 + 3)^{2} = 32 + 3

= 32 + 3

32 = 6

= 6 + 3

\frac{1400}{2400}

- 2 (k + 1) - 6 k

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What is sqrt(9+2\sqrt{18)} ?
The solution to sqrt(9+2\sqrt{18)} is sqrt(6)+sqrt(3)