What is sqrt(10+8\sqrt{2+\sqrt{9+4\sqrt{2)}}} ?

The solution to sqrt(10+8\sqrt{2+\sqrt{9+4\sqrt{2)}}} is sqrt(2)+4

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simplify sqrt(10+8\sqrt{2+\sqrt{9+4\sqrt{2)}}}

simplify

10 + 8 2 + 9 + 42

2 + 4

Decimal Notation

5.41421 \dots

Solution steps

10 + 8 2 + 9 + 42

10 + 8 2 + 9 + 42 = 18 + 82

= 18 + 82

= 2 + 82 + 16

= (2)^{2} + 82 + (16)^{2}

16 = 4

= (2)^{2} + 82 + 4^{2}

22 \cdot 4 = 82

= (2)^{2} + 22 \cdot 4 + 4^{2}

Apply Perfect Square Formula:

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

(2)^{2} + 22 \cdot 4 + 4^{2} = (2 + 4)^{2}

= (2 + 4)^{2}

Apply radical rule:

(2 + 4)^{2} = 2 + 4

= 2 + 4

(3 + 7 i) - (8 - 2 i)

\frac{2}{3} \times 7

5 x^{3} - 125 x

What is sqrt(10+8\sqrt{2+\sqrt{9+4\sqrt{2)}}} ?
The solution to sqrt(10+8\sqrt{2+\sqrt{9+4\sqrt{2)}}} is sqrt(2)+4