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Algebra 3/4 : Algebra 3/4

Study concepts, example questions & explanations for Algebra 3/4

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All Algebra 3/4 Resources

6 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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Example Question #2 : Simplify Radical Expressions

Simplify the following radical expression.

$\sqrt{512}+\sqrt{68}$

Possible Answers:

$2\sqrt{16}+2\sqrt{17}$

$16\sqrt{2}+2\sqrt{17}$

$18\sqrt{19}$

$16\sqrt{17}+2\sqrt{2}$

$2\sqrt{16}+17\sqrt{2}$

Correct answer:

$16\sqrt{2}+2\sqrt{17}$

Explanation:

To simplify the radical expression look at the factors under each radical.

$\sqrt{512}+\sqrt{68}$

$\sqrt{16\cdot 16\cdot 2}+\sqrt{4\cdot 17}$

Recall that 16 and 4 are perfect squares.

$16\sqrt{2}+2\sqrt{17}$

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Example Question #3 : Simplify Radical Expressions

Simplify the following radical expression.

$\sqrt{125}+\sqrt{48}$

Possible Answers:

$5\sqrt{5}+8\sqrt{3}$

$5\sqrt{5}+2\sqrt{12}$

$5\sqrt{5}+4\sqrt{3}$

$25\sqrt{5}+4\sqrt{3}$

$25\sqrt{5}+16\sqrt{3}$

Correct answer:

$5\sqrt{5}+4\sqrt{3}$

Explanation:

To simplify the radical expression look at the factors under each radical.

$\sqrt{125}+\sqrt{48}$

$\sqrt{25\cdot 5}+\sqrt{4\cdot 12}$

Recall that 25 and 4 are perfect squares.

$5\sqrt{5}+2\sqrt{12}$

From here 12 can be factored further.

$\\5\sqrt{5}+2\sqrt{4\cdot 3} \\5\sqrt{5}+2\cdot 2\sqrt{3} \\5\sqrt{5}+4\sqrt{3}$

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Example Question #4 : Simplify Radical Expressions

Simplify the following radical expression.

$\sqrt{512}+\sqrt{68}$

Possible Answers:

$16\sqrt{17}+2\sqrt{2}$

$18\sqrt{19}$

$2\sqrt{16}+17\sqrt{2}$

$2\sqrt{16}+2\sqrt{17}$

$16\sqrt{2}+2\sqrt{17}$

Correct answer:

$16\sqrt{2}+2\sqrt{17}$

Explanation:

To simplify the radical expression look at the factors under each radical.

$\sqrt{512}+\sqrt{68}$

$\sqrt{16\cdot 16\cdot 2}+\sqrt{4\cdot 17}$

Recall that 16 and 4 are perfect squares.

$16\sqrt{2}+2\sqrt{17}$

Report an Error

Example Question #1 : Properties Of Logarithms & Exponents

Convert the expression from logarithmic to exponential.

$\log_6 216=3$

Possible Answers:

$216=3^{1/6}$

6^3=216

$216^{1/6}=3$

3^6=216

$216=6^{1/3}$

Correct answer:

6^3=216

Explanation:

To convert the logarithmic expression to exponential form, recall the change of base formula.

$\log_b a=c\rightarrow b^c=a$

Apply the change of base formula to this particular logarithmic expression.

$\log_6 216=3$

$\\b=6 \\a=216 \\c=3$

The exponential form becomes

6^3=216

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Example Question #2 : Properties Of Logarithms & Exponents

Convert the expression from logarithmic to exponential.

$\log_4 1024=5$

Possible Answers:

5^4=1020

5^4=1024

$1024^\frac{1}{4}=5$

4^5=1024

4^5=1025

Correct answer:

4^5=1024

Explanation:

To convert the logarithmic expression to exponential form, recall the change of base formula.

$\log_b a=c\rightarrow b^c=a$

Apply the change of base formula to this particular logarithmic expression.

$\log_4 1024=5$

$\\b=4 \\a=1024 \\c=5$

The exponential form becomes

4^5=1024

Report an Error

Example Question #3 : Properties Of Logarithms & Exponents

Convert the expression from logarithmic to exponential.

$\log_3 9=2$

Possible Answers:

3^2=9

3^3=9

9^2=3

$9^\frac{1}{3}=2$

2^3=9

Correct answer:

3^2=9

Explanation:

To convert the logarithmic expression to exponential form, recall the change of base formula.

$\log_b a=c\rightarrow b^c=a$

Apply the change of base formula to this particular logarithmic expression.

$\log_3 9=2$

$\\b=3 \\a=9 \\c=2$

The exponential form becomes

3^2=9

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Example Question #4 : Properties Of Logarithms & Exponents

Convert the expression from logarithmic to exponential.

$\log_6 216=3$

Possible Answers:

$216^{1/6}=3$

$216=3^{1/6}$

$216=6^{1/3}$

6^3=216

3^6=216

Correct answer:

6^3=216

Explanation:

To convert the logarithmic expression to exponential form, recall the change of base formula.

$\log_b a=c\rightarrow b^c=a$

Apply the change of base formula to this particular logarithmic expression.

$\log_6 216=3$

$\\b=6 \\a=216 \\c=3$

The exponential form becomes

6^3=216

Report an Error

Example Question #5 : Properties Of Logarithms & Exponents

Convert the expression from logarithmic to exponential.

$\log_4 1024=5$

Possible Answers:

5^4=1020

4^5=1024

$1024^\frac{1}{4}=5$

5^4=1024

4^5=1025

Correct answer:

4^5=1024

Explanation:

To convert the logarithmic expression to exponential form, recall the change of base formula.

$\log_b a=c\rightarrow b^c=a$

Apply the change of base formula to this particular logarithmic expression.

$\log_4 1024=5$

$\\b=4 \\a=1024 \\c=5$

The exponential form becomes

4^5=1024

Report an Error

Example Question #1 : Basic Trigonometry

What is the degree equivalent for an angle that is $\frac{\pi}{2}$ radians?

Possible Answers:

$90^\circ$

$135^\circ$

$45^\circ$

$180^\circ$

$30^\circ$

Correct answer:

$90^\circ$

Explanation:

To find the degree equivalent for an angle that is $\frac{\pi}{2}$ radians first recall the unit conversion between degrees and radians.

There are 360 degrees or $2\pi$ radians in a circle.

When simplified this is,

$\pi=180^\circ$

therefore to convert from radians to degrees, simply multiply by $\frac{180^\circ}{\pi}$ .

$\frac{\pi}{2}\times \frac{180^\circ}{\pi}$

$\frac{180^\circ}{2}=90^\circ$

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Example Question #2 : Basic Trigonometry

What is the degree equivalent for an angle that is $\frac{3\pi}{2}$ radians?

Possible Answers:

$270^\circ$

$315^\circ$

$135^\circ$

$180^\circ$

$150^\circ$

Correct answer:

$270^\circ$

Explanation:

To find the degree equivalent for an angle that is $\frac{\pi}{2}$ radians first recall the unit conversion between degrees and radians.

There are 360 degrees or $2\pi$ radians in a circle.

When simplified this is,

$\pi=180^\circ$

therefore to convert from radians to degrees, simply multiply by $\frac{180^\circ}{\pi}$ .

$\frac{3\pi}{2}\times \frac{180^\circ}{\pi}$

$\frac{3\cdot 180^\circ}{2}=270^\circ$

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Algebra 3/4 : Algebra 3/4

Study concepts, example questions & explanations for Algebra 3/4

All Algebra 3/4 Resources

Example Questions

Example Question #2 : Simplify Radical Expressions

Example Question #3 : Simplify Radical Expressions

Example Question #4 : Simplify Radical Expressions

Example Question #1 : Properties Of Logarithms & Exponents

Example Question #2 : Properties Of Logarithms & Exponents

Example Question #3 : Properties Of Logarithms & Exponents

Example Question #4 : Properties Of Logarithms & Exponents

Example Question #5 : Properties Of Logarithms & Exponents

Example Question #1 : Basic Trigonometry

Example Question #2 : Basic Trigonometry

All Algebra 3/4 Resources

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