What is sqrt(17+12\sqrt{2)} ?

The solution to sqrt(17+12\sqrt{2)} is 2sqrt(2)+3

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Popular >

simplify sqrt(17+12\sqrt{2)}

simplify

17 + 122

22 + 3

Decimal Notation

5.82842 \dots

Solution steps

17 + 122

= 8 + 122 + 9

= 4 \cdot 2 + 122 + 9

= (4)^{2} (2)^{2} + 122 + (9)^{2}

4 = 2

9 = 3

= 2^{2} (2)^{2} + 122 + 3^{2}

2 \cdot 22 \cdot 3 = 122

= (22)^{2} + 2 \cdot 22 \cdot 3 + 3^{2}

Apply Perfect Square Formula:

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

(22)^{2} + 2 \cdot 22 \cdot 3 + 3^{2} = (22 + 3)^{2}

= (22 + 3)^{2}

Apply radical rule:

(22 + 3)^{2} = 22 + 3

= 22 + 3

1.2 \cdot 1 0^{4}

30 a x + 55 b x

\frac{1}{2} (9.81)

2 x^{4} + 3 x^{3} - 6 x^{2} - 9 x

- 0.04