What is sqrt(6-4\sqrt{2)} ?

The solution to sqrt(6-4\sqrt{2)} is 2-sqrt(2)

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Popular >

simplify sqrt(6-4\sqrt{2)}

simplify

6 - 42

2 - 2

Decimal Notation

0.58578 \dots

Solution steps

6 - 42

= 2 - 42 + 4

= (2)^{2} - 42 + (4)^{2}

4 = 2

= (2)^{2} - 42 + 2^{2}

22 \cdot 2 = 42

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

Apply Perfect Square Formula:

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

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

= (2 - 2)^{2}

Apply exponent rule:

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

n

is even

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

= (2 - 2)^{2}

Apply radical rule:

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

= 2 - 2

12 x^{2} + 10 x - 8

39 + 316

\frac{7 b}{b + 2} - \frac{3}{b + 5}

23 \cdot 27

27 \times 7