Question

rationalise and simplify √3-√2/√3+√2​

Answer 1

◐ Given :–

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Dimensions of a brick = 25 cm × 15 cm × 8 cm.

Dimensions of the wall = 10 m × 4 m × 5 m.

\dfrac{1}{10}101 of its volume is occupied by mortar.

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◐ To Find :–

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The number of bricks required to build the wall.

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◐ Solution :–

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» We would first find the volume of a brick.

» Then, we would find the volume of the wall.

» Since {\dfrac{1}{10}}^{th}101th of the volume is occupied by the mortar, so, we would find the remaining volume.

» After finding the remaining volume, we would divide it by the volume of a brick so as to get the number of bricks.

\begin{gathered} \\ \end{gathered}

◆ Finding the Volume of a Brick :

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We have :

Length = 25 cm

Breadth = 15 cm

Height = 8 cm

We know -

\odot\;\boxed{\sf Volume_{\:cuboid}=Length\times Breadth \times Height }⊙Volumecuboid=Length×Breadth×Height

So,

\begin{gathered} \colon \rarr \sf \: volume _{ \: brick} = 25 \times 15 \times 8 \: {cm}^{3} \\ \\ \colon \dashrightarrow \boxed{ \pink{\frak{volume _{ \: brick} = 3000 \: {cm}^{3} }}}\end{gathered}:→volumebrick=25×15×8cm3:⇢volumebrick=3000cm3

\begin{gathered} \\ \end{gathered}

◆ Finding the Volume of the Wall :

\begin{gathered} \\ \end{gathered}

We have :

Length = 10 m = 1000 cm

Breadth = 4 m = 400 cm

Height = 5 m = 500 cm

So,

\begin{gathered} \colon \rarr \sf \: volume _{ \: wall} = 1000 \times 400 \times 500 \: {cm}^{3} \\ \\ \colon \dashrightarrow \boxed{ \frak{ \pink{volume _{ \: wall} = 200000000 \: {cm}^{3}}}} \end{gathered}:→volumewall=1000×400×500cm3:⇢volumewall=200000000cm3

\begin{gathered} \\ \end{gathered}

◆ Finding Remaining Volume :

\begin{gathered} \\ \end{gathered}

We have :

Volume of the wall = 20,00,00,000 cm³

\dfrac{1}{10}101 of the volume is occupied by mortar.

So,

\begin{gathered} \colon \rarr \sf \: remaining \: volume = volume _{ \: wall} - \frac{1}{10} \times volume _{ \: wall} \\ \\ \colon \rarr \sf \: remaining \: volume = \frac{9}{10} \times volume _{ \: wall} \\ \\ \colon \sf \rarr \: remaining \: volume = \frac{9}{ \cancel{10}} \times 20000000 \cancel0 \: {cm}^{3} \\ \\ \colon \rarr \boxed{ \pink{ \frak{remaining \: volume = 180000000 \: {cm}^{3}}}} \end{gathered}:→remainingvolume=volumewall−101×volumewall:→remainingvolume=109×volumewall:→remainingvolume=109×200000000cm3:→remainingvolume=1

Answer 2

Step-by-step explanation:

$\frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \\ = \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \times \frac{ \sqrt{3 } - \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \\ = \frac{3 + 2 - 2 \sqrt{6} }{3 - 2} \\ = \frac{5 - 2 \sqrt{6} }{1} = 5 - 2 \sqrt{6}$