Tag: decimal forms

Questions Related to decimal forms

Find the values of each of the following correct to three places of decimals, it being given that $ \sqrt{2}=1.4142, \sqrt{3} = 1.732, \sqrt{5} = 2.2360, \sqrt{6} = 2.4495$ and $\sqrt{10} = 3.162.$ 


$\dfrac{1+\sqrt{2}}{3-2\sqrt{2}}$

maths decimal forms comparing and ordering of decimals more or less comparing decimals

  1. 14.0710

  2. 24.10710

  3. 16.0213

  4. None of the above

Show answer
Correct Option: A
Explanation:
Given,

$\dfrac{1+\sqrt 2}{3-2 \sqrt 2}$

$=\dfrac{1+\sqrt 2}{\sqrt 3 \times \sqrt 3-\sqrt 2 \times \sqrt 2 \times \sqrt 2}$

$=\dfrac{1+1.4142}{1.732 \times 1.732-1.4142 \times 1.4142 \times 1.4142}$

$=14.0710$

Find the value of the following correct to three places of decimals, it being given that $ \sqrt{2}=1.4142, \sqrt{3} = 1.732, \sqrt{5} = 2.2360, \sqrt{6} = 2.4495$ and $\sqrt{10} = 3.162.$ 


$\dfrac{3-\sqrt{5}}{3+2\sqrt{5}}$

maths decimal forms comparing and ordering of decimals more or less comparing decimals

  1. 0.102

  2. 2.1102

  3. 1.1002

  4. None of the above

Show answer
Correct Option: A
Explanation:
Given,

$\dfrac {3-\sqrt 5}{3+2\sqrt{5}}$

$=\dfrac {\sqrt{3}\times \sqrt{3}-\sqrt 5}{\sqrt{3}\times \sqrt{3}+\sqrt{2}\times \sqrt{2} \times \sqrt{5}}$

$=\dfrac {1.732\times 1.732-2.2360}{1.732\times 1.732+1.4142\times 1.4142 \times 2.2360}$

$=0.102$