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Nelson Calculus and Vectors

Chris Kirkpatrick, Peter Crippin

Chapter 1

Assessing Atheletic Performance - all with Video Answers

Educators

Section 1

Radical Expressions: Rationalizing Denominators

02:11

Problem 1

Write the conjugate of each radical expression.
a. $2 \sqrt{3}-4$
b. $\sqrt{3}+\sqrt{2}$
c. $-2 \sqrt{3}-\sqrt{2}$
d. $3 \sqrt{3}+\sqrt{2}$
e. $\sqrt{2}-\sqrt{5}$
f. $-\sqrt{5}+2 \sqrt{2}$

Leonardo Schultz
Leonardo Schultz
Numerade Educator
04:10

Problem 2

Rationalize the denominator of each expression. Write your answer in simplest form.
a. $\frac{\sqrt{3}+\sqrt{5}}{\sqrt{2}}$
b. $\frac{2 \sqrt{3}-3 \sqrt{2}}{\sqrt{2}}$
c. $\frac{4 \sqrt{3}+3 \sqrt{2}}{2 \sqrt{3}}$
d. $\frac{3 \sqrt{5}-\sqrt{2}}{2 \sqrt{2}}$

Leonardo Schultz
Leonardo Schultz
Numerade Educator
07:51

Problem 3

Rationalize each denominator.
a. $\frac{3}{\sqrt{5}-\sqrt{2}}$
b. $\frac{2 \sqrt{5}}{2 \sqrt{5}+3 \sqrt{2}}$
c. $\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$
d. $\frac{2 \sqrt{5}-8}{2 \sqrt{5}+3}$
e. $\frac{2 \sqrt{3}-\sqrt{2}}{5 \sqrt{2}+\sqrt{3}}$
f. $\frac{3 \sqrt{3}-2 \sqrt{2}}{3 \sqrt{3}+2 \sqrt{2}}$

Leonardo Schultz
Leonardo Schultz
Numerade Educator
03:28

Problem 4

Rationalize each numerator.
a. $\frac{\sqrt{5}-1}{4}$
b. $\frac{2-3 \sqrt{2}}{2}$
c. $\frac{\sqrt{5}+2}{2 \sqrt{5}-1}$

Leonardo Schultz
Leonardo Schultz
Numerade Educator
04:07

Problem 5

a. Rationalize the denominator of $\frac{8 \sqrt{2}}{\sqrt{20}-\sqrt{18}}$
b. Rationalize the denominator of $\frac{8 \sqrt{2}}{2 \sqrt{5}-3 \sqrt{2}}$
c. Why are your answers in parts a and b the same? Explain.

Leonardo Schultz
Leonardo Schultz
Numerade Educator
09:01

Problem 6

Rationalize each denominator.
a. $\frac{2 \sqrt{2}}{2 \sqrt{3}-\sqrt{8}}$
b. $\frac{2 \sqrt{6}}{2 \sqrt{27}-\sqrt{8}}$
c. $\frac{2 \sqrt{2}}{\sqrt{16}-\sqrt{12}}$
d. $\frac{3 \sqrt{2}+2 \sqrt{3}}{\sqrt{12}-\sqrt{8}}$
e. $\frac{3 \sqrt{5}}{4 \sqrt{3}-5 \sqrt{2}}$
f. $\frac{\sqrt{18}+\sqrt{12}}{\sqrt{18}-\sqrt{12}}$

Leonardo Schultz
Leonardo Schultz
Numerade Educator
02:20

Problem 7

Rationalize the numerator of each of the following expressions:
a. $\frac{\sqrt{a}-2}{a-4}$
b. $\frac{\sqrt{x+4}-2}{x}$
c. $\frac{\sqrt{x+h}-x}{x}$

Leonardo Schultz
Leonardo Schultz
Numerade Educator