Question

Square root of -180 times square root of 10what is the answer

Answer 1

When multiplying two square roots, multiply the numbers inside the roots and then solve the problem:

`\sqrt[]{a}\cdot\sqrt[]{b}=\sqrt[]{a\cdot b}`

In this problem:

`\sqrt[]{-180}\cdot\sqrt[]{10}=\sqrt[]{-1800}`

Using the same rule above, you can divide the square root into 1800 and -1:

`\sqrt[]{-1800}=\cdot\sqrt[]{1800}\cdot\sqrt[]{-1}`

Using i = √-1

`\sqrt[]{1800}\cdot i`

Now, let's factor 1800:

1800 |2

900 |2

450 |2

225 |3

75 |3

25 |5

5 |5

1

So, 1800 = 2*2*2*3*3*5*5

Then,

`\begin{gathered} \sqrt[]{1800}i=\sqrt[]{2\cdot2\cdot2\cdot3\cdot3\cdot5\cdot5}i \\ =2\cdot3\cdot5\cdot\sqrt[]{2}i \\ =30i\sqrt[]{2} \end{gathered}`

Answer: 30i√2.