Use the product rule to multiply the following. 5 x ⋅ 7 y \sqrt{5x}\cdot\sqrt{7y}

we're asked to use the product rule to multiply the following. We have the square root of five X times the square root of seven Y. So now we're throwing some variables into the mix, but we can still use our product rule in the same way. In order to condense these two square roots being multiplied into one, I wanna do that multiplication underneath one radical. So that makes this the square root of five x times seven y. Now we can do some further simplification here by going ahead and multiplying those constants five times seven in order to get us 35. So this becomes the square root of 35 x y. And this is my solution here, having used the product rule to perform that multiplication. I'll see you in the next one.

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1. Whole Numbers2h 43m

Adding Whole Numbers
27m

Subtracting Whole Numbers
21m

Multiplying Whole Numbers
46m

Dividing Whole Numbers
21m

Long Division
36m

Exponents
10m

2. Integers1h 7m

Introduction to Integers
16m

Multiplying Integers
24m

Exponential Expressions
10m

Dividing Integers
16m

3. Introduction to Solving Equations and Problem Solving1h 11m

Simplifying Expressions
13m

Translating Word Phrases to Algebraic Expressions
6m

Introduction to Solving Equations
41m

Translating Sentences to Algebraic Equations
9m

4. Fractions1h 29m

Intro To Fractions and Mixed Numbers
44m

Simplifying Fractions
45m

5. Decimals1h 20m

Introduction to Decimals
26m

Rounding Decimals
12m

Adding And Subtracting Decimals
41m

6. Ratio, Proportion, and Percent2h 1m

Ratios and Rates
35m

Proportions
33m

Solving Percent Problems With Equations
16m

Applications of Percent
36m

7. Graphing and Introduction to Statistics31m

Tables
3m

Bar Graphs
3m

Frequency Distributions and Histograms
5m

Line Graphs
14m

Circle Graphs
4m

8. Geometry49m

Square Roots and The Pythagorean Theorem
29m

The Circle
20m

9. Measurement58m

US Units of Length
25m

Metric Units of Length
33m

10. Linear Equations and Inequalities6h 29m

The Distributive Property
17m

Evaluating Expressions
15m

Review: Addition and Subtraction Properties of Equality
41m

Review: Multiplication and Division Properties of Equality
30m

Solving Linear Equations
1h 14m

Introduction to Problem Solving
37m

Formulas
21m

Review: Percent Problem Solving
59m

Mixture Problem Solving
43m

Linear Inequalities in One Variable
46m

11. Graphing Linear Equations and Inequalities4h 58m

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
57m

Function Notation
15m

12. Systems of Linear Equations1h 43m

Solving Systems of Linear Equations by Graphing
41m

Solving Systems of Linear Equations by Substitution
15m

Solving Systems of Linear Equations by Elimination
45m

13. Exponents and Polynomials3h 55m

Review: Evaluating Exponents
29m

The Product Rule
10m

Intro to the Power Rules
18m

The Power of a Quotient Rule
18m

Negative Exponents
28m

The Quotient Rule
13m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
21m

Adding and Subtracting Polynomials
20m

Multiplying Polynomials
33m

Special Products
34m

14. Factoring Polynomials2h 42m

Factoring by Greatest Common Factor & Grouping
38m

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

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

Factoring Special Products
20m

Sum & Difference of Cubes
12m

Quadratic Equations & Applications
41m

15. Rational Expressions and Equations3h 40m

Simplifying Rational Expressions
39m

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

16. Roots and Radicals2h 46m

Introduction to Radical Expressions
47m

Simplifying Radical Expressions
46m

Adding and Subtracting Radicals
19m

Multiplying, Dividing, and Rationalizing Radicals
53m

17. Quadratic Equations1h 55m

The Square Root Property
17m

Completing the Square
26m

The Quadratic Formula
40m

Graphing Quadratic Equations
30m

16. Roots and Radicals

Simplifying Radical Expressions

Prealgebra & Beginning Algebra

16. Roots and Radicals

Simplifying Radical Expressions

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Multiple Choice

Use the product rule to multiply the following.
$\sqrt{5 x} \cdot \sqrt{7 y}$

$the square root of 35 x y$

$35 x y$

$the square root of 12 x squared y squared$

$the square root of 12 x y$

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Use the product rule to multiply the following.5x⋅7y\(\sqrt{5x}\[\cdot\]\sqrt{7y}\)

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Use the product rule to multiply the following.
$\sqrt{5 x} \cdot \sqrt{7 y}$