State true or false -2 - 1-2 is irrational-

The correct option is A True √(2)→ irrational number 1 √(2)=√(2)2→ irrational number Sum of two irrational numbers is an irrational number. Thus given ...

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Byju's Answer

Standard X

Mathematics

Number Theory: Interesting Results

State true or...

Question

State true or false
$\sqrt{2} + \frac{1}{\sqrt{2}}$ is irrational.

True

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False

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Solution

The correct option is A True
$\sqrt{2} \to i r r a t i o n a l n u m b e r \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2} \to i r r a t i o n a l n u m b e r$

Sum of two irrational numbers is an irrational number. Thus given number is an irrational number.

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State true or false√2+1√2 is irrational.

The correct option is A True√2→irrational number1√2=√22→irrational numberSum of two irrational numbers is an irrational number. Thus given number is an irrational number.

State true or false
$\sqrt{2} + \frac{1}{\sqrt{2}}$ is irrational.

The correct option is A True
$\sqrt{2} \to i r r a t i o n a l n u m b e r \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2} \to i r r a t i o n a l n u m b e r$

Sum of two irrational numbers is an irrational number. Thus given number is an irrational number.