What is (sqrt(5+\sqrt{24)}+sqrt(5-\sqrt{24)})^2 ?

The solution to (sqrt(5+\sqrt{24)}+sqrt(5-\sqrt{24)})^2 is 12

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simplify (sqrt(5+\sqrt{24)}+sqrt(5-\sqrt{24)})^2

simplify

(5 + 24 + 5 - 24)^{2}

12

Solution steps

(5 + 24 + 5 - 24)^{2}

Apply Perfect Square Formula:

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

(5 + 24 + 5 - 24)^{2} = (5 + 24)^{2} + 2 5 + 24 5 - 24 + (5 - 24)^{2}

= (5 + 24)^{2} + 2 5 + 24 5 - 24 + (5 - 24)^{2}

(5 + 24)^{2} + 2 5 + 24 5 - 24 + (5 - 24)^{2} = 10 + 2 5 + 24 5 - 24

= 10 + 2 5 + 24 5 - 24

2 5 + 24 5 - 24 = 2

= 10 + 2

Add the numbers:

10 + 2 = 12

= 12

192 a^{36} b^{9}

\frac{p ^{2} + p}{2 p}

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\frac{4 x ^{2}}{28 y ^{4} z ^{5}}

What is (sqrt(5+\sqrt{24)}+sqrt(5-\sqrt{24)})^2 ?
The solution to (sqrt(5+\sqrt{24)}+sqrt(5-\sqrt{24)})^2 is 12