What is sqrt(8-\sqrt{28)} ?

The solution to sqrt(8-\sqrt{28)} is sqrt(7)-1

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simplify sqrt(8-\sqrt{28)}

simplify

8 - 28

7 - 1

Solution steps

8 - 28

28 = 27

= 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

\frac{11}{7} + \frac{\frac{4}{5}}{\frac{7}{2}}

x^{2} x^{7}

2 \frac{1}{2} \div 6

(2 x + 1) (x^{2} - x - 7)

- 6 \times 7