Question

Сравните числа корень из50 +корень из 48 сравнить с 14

Answer 1

√50+√48 и 14
Возведем обе части в квадрат:
(√50+√48)²=50+2√(50*48)+48=98+2√2400
14²=196
98+2√2400 и 196  |-98
2√2400 и 98   |:2
√2400 и 49 возведем снова в квадрат
2400 < 2401 ⇒
√50+√48 < 14

Answer 2

I can help you compare the numbers $\sqrt{50}$, $\sqrt{48}$, and $14$. Here is a detailed explanation:

First, we can simplify the square roots by finding the largest perfect square that divides the radicand (the number under the root sign). For example, $\sqrt{50}=\sqrt{25\cdot 2}=\sqrt{25}\cdot \sqrt{2}=5\sqrt{2}$. Similarly, $\sqrt{48}=\sqrt{16\cdot 3}=\sqrt{16}\cdot \sqrt{3}=4\sqrt{3}$.

Next, we can compare the simplified square roots by using their decimal approximations. We can use a calculator or an online tool to find the decimals. For example, $5\sqrt{2}\approx 7.07$ and $4\sqrt{3}\approx 6.93$.

Finally, we can compare the decimals with $14$ and write the inequalities. For example, $5\sqrt{2}<14$ and $4\sqrt{3}<14$. Therefore, we can conclude that $\sqrt{50}<\sqrt{48}<14$.

Some additional information or tips for the user are:

- To compare square roots, we can also use the property that if $a>b>0$, then $\sqrt{a}>\sqrt{b}$. - To compare square roots with integers, we can also use the fact that $\sqrt{n}$ is an integer if and only if $n$ is a perfect square. For example, $\sqrt{49}=7$ is an integer, but $\sqrt{50}$ is not. Therefore, $\sqrt{50}<\sqrt{49}<8$. - To compare numbers with different types of roots, such as cube roots or fourth roots, we can use the same method of simplifying, approximating, and comparing. For example, to compare $\sqrt[3]{27}$, $\sqrt[4]{81}$, and $3$, we can simplify them as $3$, $3\sqrt[4]{3}$, and $3$, then approximate them as $3$, $3.76$, and $3$, and then compare them as $3<3\sqrt[4]{3}<4$.