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Popular >

simplify sqrt(\sqrt{1+x^2)}

Solution

simplify

1 + x^{2}

Solution

4 x^{2} + 1

Solution steps

1 + x^{2}

Apply radical rule:

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

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

Apply exponent rule:

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

assuming

a \geq 0

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

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

= (1 + x^{2})^{\frac{1}{4}}

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

= 4 1 + x^{2}

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Frequently Asked Questions (FAQ)

What is sqrt(\sqrt{1+x^2)} ?
The solution to sqrt(\sqrt{1+x^2)} is \sqrt[4]{x^2+1}