# Chapter P - Section P.3 - Radicals and Rational Exponents - Exercise Set - Page 46: 115

The decoded message is: Paige Fox is bad at math.

#### Work Step by Step

Decode letters A to Z as follows: \begin{align} & A=\sqrt{121} \\ & =11 \\ & B={{2}^{3}} \\ & =8 \end{align} \begin{align} & C=\sin \frac{\pi }{2} \\ & =1 \\ & D=51\div 3 \\ & =17 \end{align} \begin{align} & E=\sqrt[3]{1000} \\ & =10 \\ & F=\frac{1}{2}\left( \frac{1}{2}\left( \frac{1}{2}\left( 16 \right) \right) \right) \\ & =2 \end{align} \begin{align} & G=\frac{5}{3}+\frac{5}{3}+\frac{5}{3} \\ & =5 \\ & H=4205-4186 \\ & =19 \end{align} \begin{align} & I=\sqrt{13}\cdot \sqrt{13} \\ & =13 \\ & J=\frac{14}{5}\times \frac{10}{4} \\ & =13 \end{align} \begin{align} & K=\left| -26 \right| \\ & =26 \\ & L=\left( 9x+9x \right)\div 3x \\ & =6 \end{align} \begin{align} & M=\left( 9\times 11 \right)-\left( 7\times 11 \right) \\ & =22 \\ & N=\sqrt{400} \\ & =20 \end{align} \begin{align} & O=1+2+3+4+5 \\ & =15 \\ & P={{4}^{\sqrt{4}}} \\ & =16 \end{align} \begin{align} & Q=\int\limits_{0}^{2}{9{{x}^{2}}dx} \\ & =3{{x}^{2}} \\ & R=\frac{4\pi +5\pi }{\pi } \end{align} \begin{align} & S=\left( 5\times 2\times 2 \right)+3 \\ & =23 \\ & T=\sqrt{144} \\ & =12 \end{align} \begin{align} & U=-3\cos \pi \\ & =3 \\ & V={{5}^{4}}\div {{5}^{2}} \\ & 25 \end{align} \begin{align} & W={{2}^{\left( 5-3 \right)}} \\ & =4 \\ & X=9216\div 512 \\ & =18 \end{align} At last, \begin{align} & Y=\sqrt{49}\times \sqrt{9} \\ & =27 \\ & Z=\frac{14\cdot 14\cdot 14}{14\cdot 14} \\ & =14 \end{align} Now, let us consider the given message: $16-11-13-5-10-2-15-18-13-23-8-11-17-11-12-22-11-12-19$ \begin{align} & 16=P \\ & 11=a \\ & 13=i \\ & 5=g \end{align} \begin{align} & 10=e \\ & 2=f \\ & 15=0 \\ & 18=x \end{align} \begin{align} & 13=i \\ & 23=s \\ & 8=b \\ & 11=a \end{align} \begin{align} & 17=d \\ & 11=a \\ & 12=t \\ & 22=M \end{align} \begin{align} & 11=a \\ & 12=t \\ & 19=h \end{align} Hence, the decoded statement is: Paige fox is bad at Math.

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