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Michael Lugo
Michael Lugo
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user4594
user4594

Is there an algebraic solution to Showing $\sqrt{2}\sqrt{3} $ is $>$greater or $<less than $ \sqrt{2} + \sqrt{3} $ ?algebraically

I want to know how toHow can we establish algebraically if $\sqrt{2}\sqrt{3}$ is greater than or less than $\sqrt{2} + \sqrt{3}$.?

I know I can plug the values into any calculator and compare the digits, but that is not very satisfying.

  I've tried to solve $$ \sqrt{2}+\sqrt{3}+x=\sqrt{2}\sqrt{3} $$$$\sqrt{2}+\sqrt{3}+x=\sqrt{2}\sqrt{3} $$ to see if $x$ is positive or negative. But I'm just getting sums of square roots whose positive or negative values are not obvious.

Can it be done without the decimal expansion?

Is there an algebraic solution to $\sqrt{2}\sqrt{3} $ is $>$ or $< \sqrt{2} + \sqrt{3} $ ?

I want to know how to establish algebraically if $\sqrt{2}\sqrt{3}$ is greater than or less than $\sqrt{2} + \sqrt{3}$.

I know I can plug the values into any calculator and compare the digits, but that is not very satisfying.

  I've tried to solve $$ \sqrt{2}+\sqrt{3}+x=\sqrt{2}\sqrt{3} $$ to see if $x$ is positive or negative. But I'm just getting sums of square roots whose positive or negative values are not obvious.

Can it be done without the decimal expansion?

Showing $\sqrt{2}\sqrt{3} $ is greater or less than $ \sqrt{2} + \sqrt{3} $ algebraically

How can we establish algebraically if $\sqrt{2}\sqrt{3}$ is greater than or less than $\sqrt{2} + \sqrt{3}$?

I know I can plug the values into any calculator and compare the digits, but that is not very satisfying. I've tried to solve $$\sqrt{2}+\sqrt{3}+x=\sqrt{2}\sqrt{3} $$ to see if $x$ is positive or negative. But I'm just getting sums of square roots whose positive or negative values are not obvious.

Can it be done without the decimal expansion?

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Jeffrey L Whitledge
Jeffrey L Whitledge
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Is there an algebraic solution to $\sqrt{2}\sqrt{3} $ is $>$ or $< \sqrt{2} + \sqrt{3} $ ?

I want to know how to establish algebraically if $\sqrt{2}\sqrt{3}$ is greater than or less than $\sqrt{2} + \sqrt{3}$.

I know I can plug the values into any calculator and compare the digits, but that is not very satisfying.

I've tried to solve $$ \sqrt{2}+\sqrt{3}+x=\sqrt{2}\sqrt{3} $$ to see if $x$ is positive or negative. But I'm just getting sums of square roots whose positive or negative values are not obvious.

Can it be done without the decimal expansion?