Question

Which among the following is the smallest?
√18-√17
√12-√11
√29-√28
√34-√33

Answer 1

Answer:

I think 4 number ok friend

Step-by-step explanation:

please mark me brainlist answer

Answer 2

Answer:

The correct answer to this question is √34-√33.

Step-by-step explanation:

This problem can be solved by Rationalisation.

consider the first option,

$(\sqrt{18} - \sqrt{17}) *( (\sqrt{18} + \sqrt{17}) / (\sqrt{18} + \sqrt{17}) )\\\\= ( 18 - 17 ) / (\sqrt{18} + \sqrt{17})\\\\= 1 / (\sqrt{18} + \sqrt{17})$

consider the second option,

$(\sqrt{12} - \sqrt{11}) *( (\sqrt{12} + \sqrt{11}) / (\sqrt{12} + \sqrt{11}) )\\\\= ( 12 - 11 ) / (\sqrt{12} + \sqrt{11})\\\\= 1 / (\sqrt{12} + \sqrt{11})$

consider the third option,

$(\sqrt{29} - \sqrt{28}) *( (\sqrt{29} + \sqrt{28}) / (\sqrt{29} + \sqrt{28}) )\\\\= ( 29 - 28 ) / (\sqrt{29} + \sqrt{28})\\\\= 1 / (\sqrt{29} + \sqrt{28})$

consider the fourth option,

$(\sqrt{34} - \sqrt{33}) *( (\sqrt{34} + \sqrt{33}) / (\sqrt{34} + \sqrt{33}) )\\\\= ( 34 - 33 ) / (\sqrt{34} + \sqrt{33})\\\\= 1 / (\sqrt{34} + \sqrt{33})$

since all the numerators are same the result is decided by the denominator.

so, the option which is having greater denominator will become the smallest value.

In option 4 - we can observe that the values are higher than the remaining options.

∴ option 4 - √34-√33 is the smallest value.

Verification:

√18-√17 = 0.1195

√12-√11 = 0.1474

√29-√28 = 0.0936

√34-√33 = 0.0863

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