What is sqrt(9-2\sqrt{8)} ?

The solution to sqrt(9-2\sqrt{8)} is 2sqrt(2)-1

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simplify sqrt(9-2\sqrt{8)}

simplify

9 - 28

22 - 1

Solution steps

9 - 28

= 8 - 28 + 1

= (8)^{2} - 28 + (1)^{2}

1 = 1

= (8)^{2} - 28 + 1^{2}

28 \cdot 1 = 42

= (8)^{2} - 28 \cdot 1 + 1^{2}

Apply Perfect Square Formula:

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

(8)^{2} - 28 \cdot 1 + 1^{2} = (8 - 1)^{2}

= (8 - 1)^{2}

Apply radical rule:

(8 - 1)^{2} = 8 - 1

= 8 - 1

8 = 22

= 22 - 1

(5 - 6 i) + (3 + 2 i)

5. 5^{2} + 4. 8^{2}

2 5^{- 4^{- 2^{- 1}}}

- \frac{2 5}{5}

\frac{\frac{7}{3}}{2}