QuestionSimplify: $\frac{2 \sqrt{8}}{3}-\frac{3 \sqrt{18}}{5}-\frac{\sqrt{50}}{2}$ .

Studdy Solution

STEP 1

Assumptions1. The given expression is $\frac{ \sqrt{8}}{3}-\frac{3 \sqrt{18}}{5}-\frac{\sqrt{50}}{}$ . We need to simplify this expression3. We know that $\sqrt{ab} = \sqrt{a} \times \sqrt{b}$ and \sqrt{a^} = a

STEP 2

First, we need to simplify the square roots in the expression. Let's start with $\sqrt{8}$ .
$\sqrt{8} = \sqrt{4 \times2} = \sqrt{4} \times \sqrt{2} =2\sqrt{2}$

STEP 3

Substitute $\sqrt{8}$ with $2\sqrt{2}$ in the expression.
$\frac{2 \sqrt{8}}{3}-\frac{3 \sqrt{18}}{5}-\frac{\sqrt{50}}{2} = \frac{2 \times2\sqrt{2}}{3}-\frac{3 \sqrt{18}}{5}-\frac{\sqrt{50}}{2}$

STEP 4

implify the first term.
$\frac{2 \times2\sqrt{2}}{3} = \frac{4\sqrt{2}}{3}$

STEP 5

Next, simplify $\sqrt{18}$ .
$\sqrt{18} = \sqrt{9 \times2} = \sqrt{9} \times \sqrt{2} =3\sqrt{2}$

STEP 6

Substitute $\sqrt{18}$ with $3\sqrt{2}$ in the expression.
$\frac{4\sqrt{2}}{3}-\frac{3 \sqrt{18}}{5}-\frac{\sqrt{50}}{2} = \frac{4\sqrt{2}}{3}-\frac{3 \times3\sqrt{2}}{5}-\frac{\sqrt{50}}{2}$

STEP 7

implify the second term.
$\frac{3 \times3\sqrt{2}}{5} = \frac{9\sqrt{2}}{5}$

STEP 8

Finally, simplify $\sqrt{50}$ .
$\sqrt{50} = \sqrt{25 \times2} = \sqrt{25} \times \sqrt{2} =5\sqrt{2}$

STEP 9

Substitute $\sqrt{50}$ with $5\sqrt{2}$ in the expression.
$\frac{4\sqrt{2}}{3}-\frac{9\sqrt{2}}{5}-\frac{\sqrt{50}}{2} = \frac{4\sqrt{2}}{3}-\frac{9\sqrt{2}}{5}-\frac{5\sqrt{2}}{2}$

STEP 10

Now, we have the expression in the form of $\frac{a\sqrt{2}}{b}-\frac{c\sqrt{2}}{d}-\frac{e\sqrt{2}}{f}$ . We can simplify this by taking $\sqrt{2}$ common.
$\frac{4\sqrt{2}}{3}-\frac{9\sqrt{2}}{5}-\frac{5\sqrt{2}}{2} = \sqrt{2} \left(\frac{4}{3}-\frac{9}{5}-\frac{5}{2}\right)$

STEP 11

Now, we just need to simplify the expression inside the brackets.
$\frac{4}{3}-\frac{9}{5}-\frac{5}{} = \frac{20}{15}-\frac{27}{15}-\frac{37.5}{15} = \frac{-44.5}{15} = -3$

STEP 12

Substitute the value back into the expression.
$\sqrt{2} \left(\frac{4}{}-\frac{9}{5}-\frac{5}{2}\right) = \sqrt{2} \times - = -\sqrt{2}$ So, the simplified form of the given expression is $-\sqrt{2}$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms