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Polynomials

Question
CBSEENMA9001489
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How many irrational numbers lie between square root of 2 and square root of 3 ? Find any three irrational numbers lying between square root of 2 and square root of 3.

Solution

Infinitely many irrational numbers lie between square root of 2 and square root of 3.

One irrational number between square root of 2 and square root of 3 is
square root of square root of 2 space square root of 3 end root space equals square root of square root of 6 end root space equals space 1 over 6 to the power of 4
Another irrational number between square root of 2 and square root of 3 is square root of square root of 2 space 1 over 6 to the power of 4 end root
equals 1 over 2 to the power of 4.1 over 6 to the power of 8 equals fraction numerator 1 over denominator 2 to the power of 4. end fraction fraction numerator 1 over denominator 2 to the power of 8. end fraction 1 over 3 to the power of 8 equals space 1 over 2 to the power of 4 plus 1 over 8.1 over 3 to the power of 8 equals 2 to the power of 3 over 8 end exponent.3 to the power of 1 over 8 end exponent
Third irrational number between square root of 2 and square root of 3 is 
square root of square root of 2.2 to the power of 3 over 8 end exponent.3 to the power of 1 over 8 end exponent end root equals 2 to the power of 1 fourth end exponent.2 to the power of 3 over 16 end exponent.3 to the power of 1 over 16 end exponent equals 2 to the power of 7 over 16 end exponent.3 to the power of 1 over 16 end exponent

Some More Questions From Polynomials Chapter

Find two rational numbers between 0.1 and 0.2.

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