Simplify the following. ( 4 x ) ( 3 x y ) (4\sqrt{x})(3\sqrt{xy})

Folks. So let's take a look at our next practice problem, very similar to the last one. We're going to simplify the following expression. We've got these two terms that are multiplied. We've got four radical x times three radical x y, and we're going to simplify. Now, I don't see any pluses or minuses. There's no addition or subtraction, so so there's no distributive property we use. So what we do in these problems again is we just basically sort of drop the parentheses. We just pretend like they're not there, and we can start to multiply and rearrange the non radical terms together and then the radical terms together. So what happens here now is when I just put this equal sign, I get four times three. Those are the two non radicals times, and then I've got a radical x from the first term times a radical x y from the second term. Alright. Now obviously, what happens is four times three just becomes 12. So that's what happens outside the radical. And then over here, because of the product rule of radicals, you could just bring them all together under one. So here what happens is we have x times an x y. So basically inside of this radical here, these all these three terms are being multiplied. So one way you could also kind of write this is x times x times y. Now this x times x is just a number times itself. So another way that I could also write this is instead of x times x, I just write this as x squared times y. Alright. This is really important here because is there any other way to simplify this radical expression over here? Well, we've got the radical, we've got the square roots of some number x that's squared. A square root and a square will cancel each other out. What ends up happening here is that we pull a factor of x outside the radical because we're square rooting a number that's squared. Basically, that X just pops out of the radical over here. So here what we get is we get 12 and then we get one factor of X that's outside the radical now. But what happens to this Y that was still left inside the radical? It didn't get multiplied with anything and there's no other way to simplify it. We just simply leave it as radical y over here. There's no other way that we can make this any simpler. And so this is our final answer over here. Alright. Let me know if you have any questions. Let's move on.

Table of contents

Skip topic navigation

1. Review of Real Numbers2h 43m

Simplifying Fractions
30m

Evaluating Exponents
29m

Evaluating Expressions
15m

Translating Phrases to Expressions
16m

Translating Sentences to Equations
9m

The Distributive Property
17m

Simplifying Expressions
44m

2. Linear Equations and Inequalities5h 35m

Solving Linear Equations
2h 23m

Linear Inequalities in One Variable
46m

Set Operations and Compound Inequalities
1h 7m

Absolute Value Equations
38m

Absolute Value Inequalities
39m

3. Solving Word Problems2h 46m

Introduction to Problem Solving
37m

Formulas
25m

Percent Problem Solving
59m

Mixture Problem Solving
43m

4. Graphs and Functions5h 12m

The Rectangular Coordinate System
44m

Graph Linear Equations in Two Variables
24m

Graph Linear Equations Using Intercepts
23m

Slope of a Line
44m

Slope-Intercept Form
38m

Point Slope Form
22m

Linear Inequalities in Two Variables
28m

Introduction to Relations and Functions
53m

Function Notation
15m

Composition of Functions
17m

5. Systems of Linear Equations1h 53m

Solving Systems of Linear Equations by Graphing
29m

Solving Systems of Linear Equations by Substitution
15m

Solving Systems of Linear Equations by Elimination
45m

Systems of Linear Inequalities
23m

6. Exponents, Polynomials, and Polynomial Functions3h 17m

The Product Rule
9m

The Quotient Rule
10m

Intro to the Power Rules
17m

The Power of a Quotient Rule
13m

Negative Exponents
24m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
21m

Adding and Subtracting Polynomials
20m

Multiplying Polynomials
38m

Special Products
34m

7. Factoring2h 49m

Factoring by Greatest Common Factor & Grouping
37m

Factoring Trinomials of the Form x² + bx + c
11m

Factoring Trinomials of the Form ax² + bx + c
37m

Factoring Special Products
41m

Quadratic Equations & Applications
41m

8. Rational Expressions and Functions3h 44m

Simplifying Rational Expressions
42m

Multiplying and Dividing Rational Expressions
25m

Adding and Subtracting Rational Expressions with Common Denominators
19m

Least Common Denominators
32m

Adding and Subtracting Rational Expressions with Different Denominators
32m

Rational Equations
44m

Direct & Inverse Variation
27m

9. Roots, Radicals, and Complex Numbers3h 56m

Introduction to Radical Expressions
46m

Simplifying Radical Expressions
47m

Adding and Subtracting Radicals
19m

Multiplying, Dividing, and Rationalizing Radicals
53m

Introduction to Complex Numbers
18m

Multiplying and Dividing Complex Numbers
51m

10. Quadratic Equations and Functions3h 1m

The Square Root Property
25m

Completing the Square
26m

The Quadratic Formula
40m

Graphing Quadratic Equations
1h 28m

11. Inverse, Exponential, & Logarithmic Functions2h 31m

Introduction to Inverse Functions
25m

Exponential Functions
35m

Introduction to Logarithmic Functions
33m

Properties of Logarithms
55m

12. Conic Sections & Systems of Nonlinear Equations58m

Graphing Circles
32m

Ellipses
15m

Parabolas
10m

13. Sequences, Series, and the Binomial Theorem1h 51m

Introduction to Sequences
40m

Arithmetic Sequences
27m

Geometric Sequences
29m

Factorials
13m

9. Roots, Radicals, and Complex Numbers

Multiplying, Dividing, and Rationalizing Radicals

Intermediate Algebra

9. Roots, Radicals, and Complex Numbers

Multiplying, Dividing, and Rationalizing Radicals

Previous problemNext problem

Struggling with Intermediate Algebra?

Join thousands of students who trust us to help them ace their exams!

Multiple Choice

Simplify the following.
$(4 \sqrt{x}) (3 \sqrt{x y})$

$12x$\sqrt{y}$$

$7x$\sqrt{y}$$

$x^2y$\sqrt{12}$$

$12x^2y$

0 Comments

Previous problemNext problem

Verified step by step guidance

Start by writing the expression to simplify: $(4\sqrt{x})(3\sqrt{xy})$.

Multiply the coefficients (numbers) outside the square roots: $4 \times 3 = 12$.

Multiply the expressions inside the square roots: $\sqrt{x} \times \sqrt{xy} = \sqrt{x \times xy} = \sqrt{x^2 y}$.

Simplify the square root of $x^2 y$ by separating it into $\sqrt{x^2} \times \sqrt{y}$, which simplifies to $x \sqrt{y}$ because $\sqrt{x^2} = x$.

Combine the simplified parts: multiply the coefficient 12 by $x \sqrt{y}$ to get $12x\sqrt{y}$.

2:34m

Watch next

Master Rationalizing Denominators Example 3 with a bite sized video explanation from Patrick Ford

Struggling with Intermediate Algebra?

Simplify the following.(4x)(3xy)(4\(\sqrt{x}\))(3\(\sqrt{xy}\))

Watch next

Simplify the following.
$(4 \sqrt{x}) (3 \sqrt{x y})$