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Polynomials

Question

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Write the following in the ascend ing order of their magnitude $fourth root of 3 comma space cube root of 2 comma space cube root of 4.$

Solution

fourth root of 3 equals 3 to the power of 1 fourth end exponent equals 3 to the power of 3 over 12 end exponent equals left parenthesis 3 cubed right parenthesis to the power of 1 over 12 end exponent equals left parenthesis 27 right parenthesis to the power of 1 over 12 end exponent cube root of 2 equals 2 to the power of 1 third end exponent equals 2 to the power of 4 over 12 end exponent equals left parenthesis 2 to the power of 4 right parenthesis to the power of 1 over 12 end exponent equals left parenthesis 16 right parenthesis to the power of 1 over 12 end exponent cube root of 4 equals 4 to the power of 1 third end exponent equals 4 to the power of 4 over 12 end exponent equals left parenthesis 4 to the power of 4 right parenthesis to the power of 1 over 12 end exponent equals left parenthesis 256 right parenthesis to the power of 1 over 12 end exponent because space space space 16 less than 27 less than 256 therefore space space left parenthesis 16 right parenthesis to the power of 1 over 12 end exponent less than left parenthesis 27 right parenthesis to the power of 1 over 12 end exponent less than left parenthesis 256 right parenthesis to the power of 1 over 12 end exponent rightwards double arrow space space space space cube root of 2 space less than space fourth root of 3 less than cube root of 4

Hence, the ascending order is

cube root of 2 comma space fourth root of 3 comma cube root of 4

Some More Questions From Polynomials Chapter

Find two rational numbers between 0.1 and 0.2.

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