Question

Сравните √2+√3 и √30-√3. С объяснением.

Answer 1

$\sqrt{2}+\sqrt{3}=0.1*(\sqrt{200}+\sqrt{300})<$
$<0.1\sqrt{225}+\sqrt{324}=0.1*(15+18)=0.1*33=3.3<$
$<3.6=0.1*(54-18)=0.1*(\sqrt{2916}-\sqrt{324})<$
$<01.*(\sqrt{3000}-\sqrt{300})=\sqrt{30}-\sqrt{3}$
=====================>
$\sqrt{2}+\sqrt{3}<\sqrt{30}-\sqrt{3}$

Answer 2

Comparing √2 + √3 and √30 - √3

To compare the expressions √2 + √3 and √30 - √3, we can simplify each expression and then compare the results.

Let's start by simplifying √2 + √3:

√2 + √3 = approximately 2.41 + 1.73 = approximately 4.14

Now, let's simplify √30 - √3:

√30 - √3 = approximately 5.48 - 1.73 = approximately 3.75

Therefore, √2 + √3 is approximately 4.14, while √30 - √3 is approximately 3.75.

In conclusion, √2 + √3 is greater than √30 - √3.

Please note that the values provided are approximate and rounded for simplicity.