Question

Q3. Rationalize the denominator a) 8 3 sqrt 2 + sqrt 5
$8 \div 3 \sqrt{2} + \sqrt{5}$
​

Answer 1

Step-by-step explanation:

Given:

$\frac{8}{3 \sqrt{2} + \sqrt{5} }$

To find: Rationalization

Solution:

Tip: Identity used in denominator

$(a-b)(a+b)=a^2-b^2$

To do rationalization of the given number,multiply and divide the number by RF of denominator.

$= \frac{8}{3 \sqrt{2} + \sqrt{5} } \times \frac{3 \sqrt{2} - \sqrt{5} }{3 \sqrt{2} - \sqrt{5} } \\ \\ = \frac{8(3 \sqrt{2} - 5)}{( {3 \sqrt{2}) }^{2} - ( { \sqrt{5}) }^{2} } \\ \\ = \frac{8(3 \sqrt{2} - 5)}{18 - 5 } \\ \\ = \frac{8(3 \sqrt{2} - 5) }{13}$

Final answer:

$\red{\frac{8}{3 \sqrt{2} + \sqrt{5} } = \frac{8(3 \sqrt{2} - \sqrt{5} ) }{13}}$

Hope it helps you.

To learn more on brainly:

1) rationalize denominator square root 3 minus one upon square root 3 + 1

https://brainly.in/question/4070585

2) rationalize the denominator 1/(1+√5+√3)

https://brainly.in/question/4122211

Answer 2

Answer:

=

3

2

+

5

8

×

3

2

−

5

3

2

−

5

=

(3

2

)

2

−(

5

)

2

8(3

2

−5)

=

18−5

8(3

2

−5)

=

13

8(3

2

−5)