QuestionSimplify the expression: $5 \sqrt{112 x^{3}} - 3 x \sqrt{63 x}$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $5 \sqrt{112 x^{3}}-3 x \sqrt{63 x}$ . We are asked to simplify this expression to its simplest radical form.

STEP 2

We start by simplifying each term separately. Let's start with the first term, $5 \sqrt{112 x^{}}$ . We can write112 as $16 \times7$ and $x^{}$ as $x^{2} \times x$ . So, the first term becomes $5 \sqrt{16 \times7 x^{2} x}$ .

STEP 3

We can now take the square root of16 and $x^{2}$ , which gives us and x respectively. So, the first term simplifies to 5 \timesx \sqrt{7x} =20x \sqrt{7x}.

STEP 4

Now, let's simplify the second term, $-3x \sqrt{63x}$ . We can write63 as $9 \times7$ and x as $x^{1} \times x$ . So, the second term becomes $-3x \sqrt{9 \times7 x x}$ .

STEP 5

We can now take the square root of9 and $x^{2}$ , which gives us3 and x respectively. So, the second term simplifies to $-3x \times3x \sqrt{7} = -9x^{2} \sqrt{7}$ .

STEP 6

Finally, we can combine the simplified first and second terms to get the simplified expression $20x \sqrt{x} -9x^{2} \sqrt{}$ .So, the expression $5 \sqrt{112 x^{3}}-3 x \sqrt{63 x}$ simplifies to $20x \sqrt{x} -9x^{2} \sqrt{}$ .

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