Question

Упростите выражение 3 корень из2 умножить на корень из 5 умножить на 4 корень из 10 пожжжжалуйстаааа

Answer 1

Немного проще нежели первое

$3\sqrt{2}* \sqrt{5}*4\sqrt{10}=12\sqrt{20}*\sqrt{5}=12\sqrt{100}=12*10=120$

Answer 2

I can help you with simplifying expressions. The expression you entered is:

$$3\sqrt{2}\cdot\sqrt{5}\cdot4\sqrt{10}$$

To simplify it, we can use the following property of square roots:

$$\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}$$

Applying this property to the expression, we get:

$$3\sqrt{2}\cdot\sqrt{5}\cdot4\sqrt{10}=3\cdot4\cdot\sqrt{2\cdot5\cdot10}=12\sqrt{100}$$

Now, we can simplify the square root of 100 by finding its prime factorization:

$$100=2^2\cdot5^2$$

Then, we can use another property of square roots:

$$\sqrt{a^2}=|a|$$

This means that we can take out the square factors from the square root and multiply them outside. For example:

$$\sqrt{2^2\cdot5^2}=|2|\cdot|5|=2\cdot5=10$$

Using this method, we can simplify the square root of 100 as follows:

$$\sqrt{100}=\sqrt{2^2\cdot5^2}=|2|\cdot|5|=2\cdot5=10$$

Therefore, the final simplified expression is:

$$12\sqrt{100}=12\cdot10=120$$

You can check your answer using an online calculator or a root calculator. You can also learn more about simplifying expressions with roots.

I hope this helps. If you have any other questions, feel free to ask me.