Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$53+ \sqrt{ 8 \sqrt{ 1+ } }$$

Answer

$$53+2*sqrt(2)*(1+)^(1/4)$$

Solution


Use this rule: \(\sqrt{ab}=\sqrt{a}\sqrt{b}\).
\[53+\sqrt{8}\sqrt{\sqrt{1+}}\]
Simplify  \(\sqrt{8}\)  to  \(2\sqrt{2}\).
\[53+2\sqrt{2}\sqrt{\sqrt{1+}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[53+2\sqrt{2}{(1+)}^{\frac{1\times 1}{2\times 2}}\]
Simplify  \(1\times 1\)  to  \(1\).
\[53+2\sqrt{2}\sqrt[2\times 2]{1+}\]
Simplify  \(2\times 2\)  to  \(4\).
\[53+2\sqrt{2}\sqrt[4]{1+}\]
Regroup terms.
\[53+2\sqrt[4]{1+}\sqrt{2}\]
Simplify square root.
\[53+2\sqrt{2}\sqrt[4]{1+}\]
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