Basic Maths: Test 58

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These tests focus on the basics of Maths and are meant to indicate your preparation level for the subject.
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Basic Maths: Test 58

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Question 1

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

A	158.5
B	142.5
C	148.5
D	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

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

A	8
B	10
C	12.5
D	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

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

A	142
B	20164
C	135
D	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

A	$7\frac{1}{2}$
B	$7\frac{1}{5}$
C	$4\frac{1}{5}$
D	$5\frac{1}{2}$

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