What is sqrt(8-2\sqrt{7)} ?

The solution to sqrt(8-2\sqrt{7)} is sqrt(7)-1

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Popular >

simplify sqrt(8-2\sqrt{7)}

simplify

8 - 27

7 - 1

Decimal Notation

1.64575 \dots

Solution steps

8 - 27

= 7 - 27 + 1

= (7)^{2} - 27 + (1)^{2}

1 = 1

= (7)^{2} - 27 + 1^{2}

27 \cdot 1 = 27

= (7)^{2} - 27 \cdot 1 + 1^{2}

Apply Perfect Square Formula:

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

(7)^{2} - 27 \cdot 1 + 1^{2} = (7 - 1)^{2}

= (7 - 1)^{2}

Apply radical rule:

(7 - 1)^{2} = 7 - 1

= 7 - 1

(3 x + 7) (2 x - 1)

12 + 5 (4 x - 6)

\frac{7 - 2 i}{2 + 9 i}

(2 x - 5) (x^{2} - x + 1)

10 + (- 4)