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

0.71743 \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

- 4 (- 8 w - 4 x) - 7 x - 10 (- 10 x + 8 w)

6 y - 18

3 a b^{2} - b a

2 (20 + 8)

(8 p^{2} - 4) (p - 2)

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