What is (sqrt(3+2\sqrt{2)}+sqrt(3-2\sqrt{2)})^2 ?

The solution to (sqrt(3+2\sqrt{2)}+sqrt(3-2\sqrt{2)})^2 is 8

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simplify (sqrt(3+2\sqrt{2)}+sqrt(3-2\sqrt{2)})^2

simplify

(3 + 22 + 3 - 22)^{2}

8

Solution steps

(3 + 22 + 3 - 22)^{2}

Apply Perfect Square Formula:

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

(3 + 22 + 3 - 22)^{2} = (3 + 22)^{2} + 2 3 + 22 3 - 22 + (3 - 22)^{2}

= (3 + 22)^{2} + 2 3 + 22 3 - 22 + (3 - 22)^{2}

(3 + 22)^{2} + 2 3 + 22 3 - 22 + (3 - 22)^{2} = 8

= 8

1 0^{0.25}

\frac{1}{30}

\frac{30 k ^{2} + 6 k}{5 k + k}

(7)^{2}

(m - 5) (m^{2} + 5 m - 6)

What is (sqrt(3+2\sqrt{2)}+sqrt(3-2\sqrt{2)})^2 ?
The solution to (sqrt(3+2\sqrt{2)}+sqrt(3-2\sqrt{2)})^2 is 8