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

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

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Popular >

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

simplify

17 - 122

3 - 22

Decimal Notation

0.17157 \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 exponent rule:

(- a)^{n} = a^{n},

n

is even

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

= (3 - 22)^{2}

Apply radical rule:

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

= 3 - 22

(14 c^{2} + 4 c) (2 c^{2} - 3 c)

16 x^{2} + 60 x - 100

\frac{5}{3 - 4 i} + \frac{10}{4 + 3 i}

9 175 x^{2} - 3 x 7

\frac{8}{9} + \frac{5}{12}