Example

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

Question

$$\sqrt[ 4 ]{ 144- } \sqrt[ 4 ]{ 1250 } - \sqrt[ 4 ]{ 32 } + \sqrt[ 4 ]{ 512 }$$

Answer

$$(144-)^(1/4)*5*2^(1/4)-2^(5/4)+4*2^(1/4)$$

Solution


Simplify  \(\sqrt[4]{1250}\)  to  \(5\sqrt[4]{2}\).
\[\sqrt[4]{144-}\times 5\sqrt[4]{2}-\sqrt[4]{32}+\sqrt[4]{512}\]
Simplify  \(\sqrt[4]{32}\)  to  \(2\sqrt[4]{2}\).
\[\sqrt[4]{144-}\times 5\sqrt[4]{2}-2\sqrt[4]{2}+\sqrt[4]{512}\]
Simplify  \(\sqrt[4]{512}\)  to  \(4\sqrt[4]{2}\).
\[\sqrt[4]{144-}\times 5\sqrt[4]{2}-2\sqrt[4]{2}+4\sqrt[4]{2}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\sqrt[4]{144-}\times 5\sqrt[4]{2}-{2}^{\frac{5}{4}}+4\sqrt[4]{2}\]
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