What is sqrt(\sqrt{x+\sqrt{y)}} ?

The solution to sqrt(\sqrt{x+\sqrt{y)}} is \sqrt[4]{x+sqrt(y)}

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simplify sqrt(\sqrt{x+\sqrt{y)}}

simplify

x + y

Solution steps

x + y

Apply radical rule:

a = a^{\frac{1}{2}}

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

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

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

\frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4}

= (x + y)^{\frac{1}{4}}

0.7 \cdot 1 0^{- 6}

10 e^{- 4}

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

What is sqrt(\sqrt{x+\sqrt{y)}} ?
The solution to sqrt(\sqrt{x+\sqrt{y)}} is \sqrt[4]{x+sqrt(y)}