What is sqrt(11-4\sqrt{7)} ?

The solution to sqrt(11-4\sqrt{7)} is sqrt(7)-2

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Popular >

simplify sqrt(11-4\sqrt{7)}

simplify

11 - 47

7 - 2

Decimal Notation

0.64575 \dots

Solution steps

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

f (x) = \frac{2 ^{x}}{2 ^{x + 1}}

n - (n - 1)

- \frac{5}{6 - 3}

- 2 y^{3} (- y^{3})