Question

$$\sqrt{1+\frac{49}{576}=1+\frac{x}{24}}$$

Answer

x=6197/3

Solution


Simplify  \(\sqrt{1}\)  to  \(1\).
\[1+49576=1+x\times 24\]
Regroup terms.
\[1+49576=1+24x\]
Simplify  \(1+49576\)  to  \(49577\).
\[49577=1+24x\]
Subtract \(1\) from both sides.
\[49577-1=24x\]
Simplify  \(49577-1\)  to  \(49576\).
\[49576=24x\]
Divide both sides by \(24\).
\[\frac{49576}{24}=x\]
Simplify  \(\frac{49576}{24}\)  to  \(\frac{6197}{3}\).
\[\frac{6197}{3}=x\]
Switch sides.
\[x=\frac{6197}{3}\]

Decimal Form: 2065.666667