Question

Please solve the question​

Answer 1

Rationalising Factor of (a+b)=a-b

In Question 1

$\frac{1}{ \sqrt{6} + \sqrt{5} }$

Rationalize The Given By √6-√5

$\frac{1 \times \sqrt{6} - \sqrt{5} }{ \sqrt{6} + \sqrt{5} \times \sqrt{6} - \sqrt{5} } \\ \\ \frac{ \sqrt{6} - \sqrt{5} }{( \sqrt{ {6}^{2} } - \sqrt{5} {}^{2} } \\ \\ \frac{ \sqrt{6} - \sqrt{5} }{6 - 5} \\ \\ \frac{ \sqrt{6} - \sqrt{5} }{1}$

We Get √6-√5

Value of √6=2.449

Value of √5=2.236

Subtract it

√6-√5=2.449-2.236

=0.213

Answer=0.213

In Question 2

$\frac{ 6}{ \sqrt{5} + \sqrt{3} }$

Rationalize The given by √5-√3

$\frac{6( \sqrt{5} - \sqrt{3} )}{ (\sqrt{5} + \sqrt{3}) ( \sqrt{5} - \sqrt{3} )} \\ \\ \frac{6 \sqrt{5} - 6\sqrt{3} }{ \sqrt{5 {}^{2} } - \sqrt{3 {}^{2} } } \\ \\ \frac{ 6\sqrt{5} - 6\sqrt{3} }{5 - 3} \\ \\ \frac{6 \sqrt{5} - 6 \sqrt{3} }{2}$

Value of √5=2.236

6√5=6×2.236=13.416

Value of √3=1.732

6√3=10.392

Now

6√5-6√3=13.416-10.392

=3.024

Now,

$\frac{3.024}{2} = 1.512$

Answer=1.512

In Question 3

$\frac{1}{4 \sqrt{3} - 3 \sqrt{5} }$

Rationalising Factor of a-b=a+b

Now Now Multiply Given by

4√3+3√5

$\frac{1 \times (4 \sqrt{3} + 3 \sqrt{5}) }{(4 \sqrt{3} - 3 \sqrt{5})(4 \sqrt{3} + 3 \sqrt{5} )} \\ \\ \frac{4 \sqrt{3} + 3 \sqrt{5} }{(4 \sqrt{3} ) {}^{2} - (3 \sqrt{5} ) {}^{2} } \\ \\ \frac{4 \sqrt{3} + 3 \sqrt{5} }{(16 \times 3) - (9 \times 5)} \\ \\ \frac{4 \sqrt{3} + 3 \sqrt{5} }{48 - 45} \\ \\ \frac{4 \sqrt{3} + 3 \sqrt{5} }{3}$

Value of √3=1.732

4√3=4×1.732

=6.928

Value of √5=2.236

3√5=3×2.236=6.708

4√3+3√5

=6.928+6.708

=13.636

Now

$\frac{4 \sqrt{3} + 3\sqrt{5} }{3} \\ \\ \frac{13.636}{3} =4.545$

Answer=4.545

Remember

a²-b²=(a+b)(a-b)

Rationalising Factor of (a+b)=(a-b)

Rationalising Factor of (a-b)=(a+b)