Question

Rationalize the denominator: 1 / √9−√8

Answer 1

Answer:

1/√9-√8

1/3-2√2

1(3+2√2)/(3-2√2)(3+2√2)

using ( a-b)(a+b)=a²-b²

(3+2√2)/(3)²-(2√2)²

(3+2√2)/9-8

3+2√2/1

3+2√2

Answer 2

On rationalization, the value of  1÷$\sqrt{9} -\sqrt{8}$ becomes ($\sqrt{9} +\sqrt{8}$)÷17.

Step-by-step explanation:

Given:

The expression= 1÷$\sqrt{9} -\sqrt{8}$

To find=  a rationalized form of this

Solution:

Solving the given expression,

1÷$\sqrt{9} -\sqrt{8}$

Multiplying it by  1÷$\sqrt{9} +\sqrt{8}$

1÷($\sqrt{9} -\sqrt{8}$)( $\sqrt{9} +\sqrt{8}$)

($\sqrt{9} +\sqrt{8}$)÷( $\sqrt{9} -\sqrt{8}$)($\sqrt{9} +\sqrt{8}$)

= ($\sqrt{9} +\sqrt{8}$)÷( $9^{2} -8^{2}$)

= ($\sqrt{9} +\sqrt{8}$)÷(81-64)

= ($\sqrt{9} +\sqrt{8}$)÷(17)

= ($\sqrt{9} +\sqrt{8}$)÷17

Result:

Thus, on rationalization, the value of  1÷$\sqrt{9} -\sqrt{8}$ becomes ($\sqrt{9} +\sqrt{8}$)÷17.

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