Math

QuestionSubtract the radicals: 372y32y3 \sqrt{72 y^{3}} - \sqrt{2 y}, where all variables are positive real numbers.

Studdy Solution

STEP 1

Assumptions1. All variables represent positive real numbers. The given expressions are 372y33 \sqrt{72 y^{3}} and y\sqrt{ y}

STEP 2

First, we need to simplify the radical expressions. We can do this by factoring the numbers under the square root sign and simplifying the square roots.
For the first expression, 72y \sqrt{72 y^{}}, we can factor72 as 2^ \times^2 and y^ as y2×yy^2 \times y. \sqrt{72 y^{}} = \sqrt{2^ \times^2 \times y^2 \times y}

STEP 3

Now, we can simplify the square root by taking out pairs of numbers and variables.323×32×y2×y=3×2×3×y2y=18y2y3 \sqrt{2^3 \times3^2 \times y^2 \times y} =3 \times2 \times3 \times y \sqrt{2y} =18y \sqrt{2y}

STEP 4

For the second expression, 2y\sqrt{2 y}, it is already in its simplest form.

STEP 5

Now, we can subtract the simplified expressions.
18y2y2y18y \sqrt{2y} - \sqrt{2y}

STEP 6

We can factor out the common term 2y\sqrt{2y} from both terms.
(18y1)2y(18y -1) \sqrt{2y}So, the simplified form of the given expression 372y32y3 \sqrt{72 y^{3}}-\sqrt{2 y} is (18y1)2y(18y -1) \sqrt{2y}.

Was this helpful?

Studdy solves anything!

banner

Start learning now

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

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord