What is sqrt(\sqrt{89+\sqrt{7840)}} ?

The solution to sqrt(\sqrt{89+\sqrt{7840)}} is \sqrt[4]{89+28sqrt(10)}

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simplify sqrt(\sqrt{89+\sqrt{7840)}}

simplify

89 + 7840

Decimal Notation

3.65028 \dots

Solution steps

89 + 7840

Apply radical rule:

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

= ((89 + 7840)^{\frac{1}{2}})^{\frac{1}{2}}

Apply exponent rule:

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

= (89 + 7840)^{\frac{1}{2} \cdot \frac{1}{2}}

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

= (89 + 7840)^{\frac{1}{4}}

7840 = 2810

0.5 \cdot 0.61 \cdot 4.7 \cdot 4.7 \cdot 1 0^{- 6}

(\frac{2}{3})^{- 1}

6.1 \cdot 1 0^{- 7}

What is sqrt(\sqrt{89+\sqrt{7840)}} ?
The solution to sqrt(\sqrt{89+\sqrt{7840)}} is \sqrt[4]{89+28sqrt(10)}