Question Detail

Find the value of X
\begin{aligned} \sqrt{81} + \sqrt{0.81} = 10.09 - X \end{aligned}

0.019
0.19
0.9
0.109

Answer: Option B

Explanation:

\begin{aligned}
=> \sqrt{81} + \sqrt{0.81} = 10.09 - X
\end{aligned}

\begin{aligned}
=> 9 + 0.9 = 10.09 - X
\end{aligned}

\begin{aligned}
=> X = 10.09 - 9.9 = 0.19
\end{aligned}

1. Evaluate
\begin{aligned}
\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+\sqrt{225}}}}}
\end{aligned}

Answer: Option D

Explanation:

\begin{aligned}
= \sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+\sqrt{225}}}}}
\end{aligned}

\begin{aligned}
=\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+15}}}}
\end{aligned}

\begin{aligned}
=\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+15}}}}
\end{aligned}

\begin{aligned}
=\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{169}}}}
\end{aligned}

\begin{aligned}
=\sqrt{10+\sqrt{25+\sqrt{108+13}}}
\end{aligned}

\begin{aligned}
=\sqrt{10+\sqrt{25+\sqrt{121}}}
\end{aligned}

\begin{aligned}
=\sqrt{10+\sqrt{25+11}}
\end{aligned}

\begin{aligned}
=\sqrt{10+\sqrt{36}}
\end{aligned}

\begin{aligned}
=\sqrt{10+6}
\end{aligned}

\begin{aligned}
=\sqrt{16} = 4
\end{aligned}

2. Find the value of X
\begin{aligned} \sqrt{81} + \sqrt{0.81} = 10.09 - X \end{aligned}

0.019
0.19
0.9
0.109

Answer: Option B

Explanation:

\begin{aligned}
=> \sqrt{81} + \sqrt{0.81} = 10.09 - X
\end{aligned}

\begin{aligned}
=> 9 + 0.9 = 10.09 - X
\end{aligned}

\begin{aligned}
=> X = 10.09 - 9.9 = 0.19
\end{aligned}

3. \begin{aligned} \sqrt{\frac{32.4}{x}} = 2 \end{aligned}

Answer: Option B

4. \begin{aligned}
\sqrt{41 - \sqrt{21 + \sqrt{19 - \sqrt{9}}}}
\end{aligned}

Answer: Option D

Explanation:

\begin{aligned}
= \sqrt{41 - \sqrt{21 + \sqrt{19 - 3}}}
\end{aligned}

\begin{aligned}
= \sqrt{41 - \sqrt{21 + \sqrt{16}}}
\end{aligned}

\begin{aligned}
= \sqrt{41 - \sqrt{21 + 4}}
\end{aligned}

\begin{aligned}
= \sqrt{41 - \sqrt{25}}
\end{aligned}

\begin{aligned}
= \sqrt{41 - \sqrt{25}}
\end{aligned}

\begin{aligned}
= \sqrt{41 - 5}
\end{aligned}

\begin{aligned}
= \sqrt{36} = 6
\end{aligned}