- This is an assessment test.
- These tests focus on the basics of Maths and are meant to indicate your preparation level for the subject.
- Kindly take the tests in this series with a pre-defined schedule.

## Basic Maths: Test 58

Congratulations - you have completed *Basic Maths: Test 58*.

You scored %%SCORE%% out of %%TOTAL%%.

Your performance has been rated as %%RATING%%

Your answers are highlighted below.

Question 1 |

$\sqrt{\sqrt{3721}+\sqrt{11664}}\times 8.5=?$

158.5 | |

142.5 | |

148.5 | |

110.5 |

Question 1 Explanation:

$\begin{align}
& ?=\sqrt{\sqrt{3721}+\sqrt{11664}}\times 8.5 \\
& =\sqrt{61+108}\times 8.5 \\
& =\sqrt{169}\times 8.5 \\
& =13\times 8.5=110.5 \\
\end{align}$

Question 2 |

${{2}^{3.5}}\times {{10}^{2}}\times {{30}^{2.5}}\div {{3}^{2.5}}\times {{5}^{3.5}}={{10}^{?}}$

8 | |

10 | |

12.5 | |

6.5 |

Question 2 Explanation:

\[\begin{align}
& {{2}^{3.5}}\times {{10}^{2}}\times {{30}^{2.5}}\div {{3}^{2.5}}\times {{5}^{3.5}}={{10}^{?}} \\
& \Rightarrow {{21}^{?}} \\
& =\frac{{{2}^{3.5}}\times {{2}^{2}}\times {{2}^{2.5}}\times {{3}^{2.5}}\times {{5}^{2}}\times {{5}^{2.5}}\times {{5}^{3.5}}}{{{3}^{2.5}}} \\
& ={{\left( 2 \right)}^{3.5+2.5+2}}\times {{\left( 5 \right)}^{2+2.5+3.5}} \\
& ={{\left( 2\times 5 \right)}^{8}}={{\left( 10 \right)}^{8}} \\
& \Rightarrow ?=8 \\
\end{align}\]

Question 3 |

${{\left( 46 \right)}^{2}}+{{\left( 81 \right)}^{2}}={{\left( ? \right)}^{2}}-{{\left( 97 \right)}^{2}}-2078$

142 | |

20164 | |

135 | |

24025 |

Question 3 Explanation:

$\begin{align}
& {{\left( 46 \right)}^{2}}+{{\left( 81 \right)}^{2}}={{\left( ? \right)}^{2}}-{{\left( 97 \right)}^{2}}-2078 \\
& \Rightarrow 2116+6561={{\left( ? \right)}^{2}}-9409-2078 \\
& \Rightarrow 8677={{\left( ? \right)}^{2}}-11487 \\
& \Rightarrow {{\left( ? \right)}^{2}}=8677+11487 \\
& \Rightarrow {{\left( ? \right)}^{2}}=20164 \\
& \Rightarrow ?=\sqrt{20164}=142 \\
\end{align}$

Question 4 |

${{\left( \sqrt{5}+\frac{1}{\sqrt{5}} \right)}^{2}}$ Simplifies to

$7\frac{1}{2}$ | |

$7\frac{1}{5}$ | |

$4\frac{1}{5}$ | |

$5\frac{1}{2}$ |

Question 4 Explanation:

$\begin{align}
& ={{\left( \sqrt{5}+\frac{1}{\sqrt{5}} \right)}^{2}} \\
& {{\left( \sqrt{5} \right)}^{2}}+{{\left( \frac{1}{\sqrt{5}} \right)}^{2}}+2\times \sqrt{5}\times \frac{1}{\sqrt{5}} \\
& =5+\frac{1}{5}+2=7\frac{1}{5} \\
\end{align}$

Question 5 |

$\left( 0.3\times 4+0.35\times 0.3+0.3\times 4.5+0.3\times 1.15 \right)$ is equal to

3 | |

30 | |

5 | |

7 |

Question 5 Explanation:

$\begin{align}
& =0.3\,\left( 4+0.35+4.5+1.15 \right) \\
& =0.3\times 10=3 \\
\end{align}$

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