Find the square root of:
${\text{6 + }}\sqrt {12} - \sqrt {24} - \sqrt 8 ?$
Answer
366k+ views
Hint: Try to take out common terms in order to make calculation easier.
Given: ${\text{6 + }}\sqrt {12} - \sqrt {24} - \sqrt 8 $
Rewriting above equation as:
$
\Rightarrow \sqrt {36} + \sqrt {12} - \sqrt {24} - \sqrt 8 {\text{ }}\left\{ {\because \sqrt {36} = 6} \right\} \\
\Rightarrow \sqrt {36} - \sqrt {24} + \sqrt {12} - \sqrt 8 \\
$
Taking $\sqrt {12} $ common from first two terms and $\sqrt 4 $ from other two terms, we get
$ \Rightarrow \sqrt {12} \left( {\sqrt 3 - \sqrt 2 } \right) + \sqrt 4 \left( {\sqrt 3 - \sqrt 2 } \right)$
Now, taking out $\left( {\sqrt 3 - \sqrt 2 } \right)$ common from above equation, we get:
$
\Rightarrow \left( {\sqrt {12} + \sqrt 4 } \right)\left( {\sqrt 3 - \sqrt 2 } \right) \\
\Rightarrow \sqrt 4 \left( {\sqrt 3 + \sqrt 1 } \right)\left( {\sqrt 3 - \sqrt 2 } \right){\text{ }} \ldots \left( 1 \right) \\
$
Now, we know the value of $\sqrt 3 $ is $1.732$ and of $\sqrt 2 $ is $1.414$.
Hence, putting these values in $\left( 1 \right)$, we get
$
\therefore 2 \times \left( {1.732 + 1} \right)\left( {1.732 - 1.414} \right) \\
\Rightarrow 2 \times 2.732 \times 0.318 \\
\Rightarrow 1.7375 \\
$
Note- Whenever there is a bigger term inside the square root whose value is very difficult to calculate, always try to decompose the bigger term into multiple smaller terms whose values are known to us.
Given: ${\text{6 + }}\sqrt {12} - \sqrt {24} - \sqrt 8 $
Rewriting above equation as:
$
\Rightarrow \sqrt {36} + \sqrt {12} - \sqrt {24} - \sqrt 8 {\text{ }}\left\{ {\because \sqrt {36} = 6} \right\} \\
\Rightarrow \sqrt {36} - \sqrt {24} + \sqrt {12} - \sqrt 8 \\
$
Taking $\sqrt {12} $ common from first two terms and $\sqrt 4 $ from other two terms, we get
$ \Rightarrow \sqrt {12} \left( {\sqrt 3 - \sqrt 2 } \right) + \sqrt 4 \left( {\sqrt 3 - \sqrt 2 } \right)$
Now, taking out $\left( {\sqrt 3 - \sqrt 2 } \right)$ common from above equation, we get:
$
\Rightarrow \left( {\sqrt {12} + \sqrt 4 } \right)\left( {\sqrt 3 - \sqrt 2 } \right) \\
\Rightarrow \sqrt 4 \left( {\sqrt 3 + \sqrt 1 } \right)\left( {\sqrt 3 - \sqrt 2 } \right){\text{ }} \ldots \left( 1 \right) \\
$
Now, we know the value of $\sqrt 3 $ is $1.732$ and of $\sqrt 2 $ is $1.414$.
Hence, putting these values in $\left( 1 \right)$, we get
$
\therefore 2 \times \left( {1.732 + 1} \right)\left( {1.732 - 1.414} \right) \\
\Rightarrow 2 \times 2.732 \times 0.318 \\
\Rightarrow 1.7375 \\
$
Note- Whenever there is a bigger term inside the square root whose value is very difficult to calculate, always try to decompose the bigger term into multiple smaller terms whose values are known to us.
Last updated date: 26th Sep 2023
•
Total views: 366k
•
Views today: 8.66k
Recently Updated Pages
What do you mean by public facilities

Paragraph on Friendship

Slogan on Noise Pollution

Disadvantages of Advertising

Prepare a Pocket Guide on First Aid for your School

10 Slogans on Save the Tiger

Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Why are resources distributed unequally over the e class 7 social science CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Briefly mention the contribution of TH Morgan in g class 12 biology CBSE

What is the past tense of read class 10 english CBSE
