Basic Maths: Test 54

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Basic Maths: Test 54

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Question 1

${{\left( 2457\div 91 \right)}^{\frac{1}{3}}}+{{\left( \frac{12.5\times 100}{50} \right)}^{\frac{1}{2}}}={{\left( ? \right)}^{\frac{1}{3}}}$

A	512
B	64
C	256
D	16

Question 1 Explanation:

$\begin{align} & {{\left( \frac{2457}{91} \right)}^{\frac{1}{3}}}+{{\left( 12.5\times 2 \right)}^{\frac{1}{2}}}={{\left( ? \right)}^{\frac{1}{3}}} \\ & \Rightarrow {{\left( 27 \right)}^{\frac{1}{3}}}+{{\left( 25 \right)}^{\frac{1}{2}}}={{\left( ? \right)}^{\frac{1}{3}}} \\ & \Rightarrow {{\left( {{3}^{3}} \right)}^{\frac{1}{3}}}+{{\left( {{5}^{2}} \right)}^{\frac{1}{2}}}={{\left( ? \right)}^{\frac{1}{3}}} \\ & \Rightarrow 3+5={{\left( ? \right)}^{\frac{1}{3}}} \\ & \Rightarrow {{\left( ? \right)}^{\frac{1}{3}}}=8={{\left( {{8}^{3}} \right)}^{\frac{1}{3}}} \\ & \Rightarrow ?={{8}^{3}}=512 \\ \end{align}$

Question 2

$\sqrt{{{12}^{2}}+32\div 2-{{\left( 5 \right)}^{2}}+154}={{\left( ? \right)}^{2}}$

A	18
B	$\sqrt{17}$
C	289
D	17

Question 2 Explanation:

$\begin{align} & {{?}^{2}}=\sqrt{{{12}^{2}}+32\times \frac{1}{2}-{{\left( 5 \right)}^{2}}+154} \\ & =\sqrt{144+16-25+154} \\ & =\sqrt{289}=17 \\ & \Rightarrow ?=\sqrt{17} \\ \end{align}$

Question 3

${{\left( 0.25 \right)}^{4}}\times {{\left( 0.125 \right)}^{4}}\div {{\left( 0.0625 \right)}^{4}}={{\left( 50\div 100 \right)}^{?+3}}$

A	3
B	1
C	4
D	7

Question 3 Explanation:

$\begin{align} & {{\left( {{\left( 0.5 \right)}^{2}} \right)}^{4}}\times {{\left( {{\left( 0.5 \right)}^{3}} \right)}^{4}}\div {{\left( {{\left( 0.5 \right)}^{4}} \right)}^{4}}={{\left( \frac{50}{100} \right)}^{?+3}} \\ & \Rightarrow {{0.5}^{8}}\times {{.5}^{12}}\div {{\left( 0.5 \right)}^{16}}={{\left( 0.5 \right)}^{?+3}} \\ & \Rightarrow {{\left( 0.5 \right)}^{8+12-16}}={{\left( 0.5 \right)}^{?+3}}={{\left( 0.5 \right)}^{4}} \\ & \Rightarrow ?+3=4\, \\ & \Rightarrow ?=4-3=1 \\ \end{align}$

Question 4

A	1/2
B	43/196
C	196/43
D	1

Question 4 Explanation:

Question 5

$\sqrt{\frac{0.049\times 0.576}{0.0036\times 7.84}}$ is equal to

A	1
B	1.1
C	10
D	1.11

Question 5 Explanation:

$\begin{align} & =\sqrt{\frac{0.049\times 0.576}{0.0036\times 7.84}} \\ & =\sqrt{\frac{49\times 576}{36\times 784}} \\ & =\frac{7\times 24}{6\times 28} \\ & =1 \\ \end{align}$

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