Question

rationalize the denominator 1/3√5+2√2​

Answer 1

Step-by-step explanation:

$\huge\bold{\gray{\sf{Answer:}}}$

Explanation:

Rationalising means Multiplying the numerator and denominator both by with the opposite sign of denominator.

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

Here,this identity is used:-

$\bold{\boxed{(x + y)(x - y) = {x}^{2} - {y}^{2}}}$

$= > \frac{3 \sqrt{5} - 2 \sqrt{2} }{ {(3 \sqrt{5}) }^{2} - {(2 \sqrt{2}) }^{2} }$

_________________________________

calculation:

$= > \sqrt{5} \times \sqrt{5} = 5( {5}^{ \frac{1}{2} } \times {5}^{ \frac{1}{2} } = {5}^{ \frac{1}{2} + \frac{1}{2} } = 5)$

$= > \sqrt{2} \times \sqrt{2} = 2( {2}^{ \frac{1}{2} } \times {2}^{ \frac{1}{2} } = {2}^{ \frac{1}{2} + \frac{1}{2} } = 2)$

__________________________________

$= > \frac{3 \sqrt{5} - 2 \sqrt{2} }{45 - 8}$

$\bold{= > \frac{3 \sqrt{5} - 2 \sqrt{2} }{37} }$✓

Answer 2

Answer:

=>

3

5

+2

2

1

×

3

5

−2

2

3

5

−2

2

Here,this identity is used:-

\bold{\boxed{(x + y)(x - y) = {x}^{2} - {y}^{2}}}

(x+y)(x−y)=x

2

−y

2

= > \frac{3 \sqrt{5} - 2 \sqrt{2} }{ {(3 \sqrt{5}) }^{2} - {(2 \sqrt{2}) }^{2} }=>

(3

5

)

2

−(2

2

)

2

3

5

−2

2

_________________________________

calculation:

= > \sqrt{5} \times \sqrt{5} = 5( {5}^{ \frac{1}{2} } \times {5}^{ \frac{1}{2} } = {5}^{ \frac{1}{2} + \frac{1}{2} } = 5)=>

5

×

5

=5(5

2

1

×5

2

1

=5

2

1

+

2

1

=5)

= > \sqrt{2} \times \sqrt{2} = 2( {2}^{ \frac{1}{2} } \times {2}^{ \frac{1}{2} } = {2}^{ \frac{1}{2} + \frac{1}{2} } = 2)=>

2

×

2

=2(2

2

1

×2

2

1

=2

2

1

+

2

1

=2)

__________________________________

= > \frac{3 \sqrt{5} - 2 \sqrt{2} }{45 - 8}=>

45−8

3

5

−2

2

\bold{= > \frac{3 \sqrt{5} - 2 \sqrt{2} }{37} }=>

37

3

5

−2

2

✓