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

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

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

simplify

(2 - 7)^{2}

7 - 2

Solution steps

(2 - 7)^{2}

(2 - 7)^{2} = 11 - 47

= 11 - 47

= 7 - 47 + 4

= (7)^{2} - 47 + (4)^{2}

4 = 2

= (7)^{2} - 47 + 2^{2}

27 \cdot 2 = 47

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

Apply Perfect Square Formula:

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

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

= (7 - 2)^{2}

Apply radical rule:

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

= 7 - 2

(b^{2} + 4 b + 4) (- b + 3)

\frac{16 y ^{2}}{8 y ^{2}}

(4 n - 5) (4 n - 2)

x^{2} + 2 x^{2}

(m + 3) (m - 2)

What is sqrt((2-\sqrt{7))^2} ?
The solution to sqrt((2-\sqrt{7))^2} is sqrt(7)-2