
Find the square root of:
${\text{6 + }}\sqrt {12} - \sqrt {24} - \sqrt 8 ?$
Answer
516.9k+ 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.
Recently Updated Pages
You are awaiting your class 10th results Meanwhile class 7 english CBSE

Questions & Answers - Ask your doubts

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 Science: Engaging Questions & Answers for Success

Master Class 12 Economics: Engaging Questions & Answers for Success

Master Class 12 Maths: Engaging Questions & Answers for Success

Trending doubts
Full Form of IASDMIPSIFSIRSPOLICE class 7 social science CBSE

Fill in the blanks with appropriate modals a Drivers class 7 english CBSE

What are the controls affecting the climate of Ind class 7 social science CBSE

The southernmost point of the Indian mainland is known class 7 social studies CBSE

What were the major teachings of Baba Guru Nanak class 7 social science CBSE

What was the approximate time period of the Indus Valley class 7 social science CBSE
