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Algebra 3/4 : Simplify Radical Expressions

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

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Example Questions

Example Question #1 : Simplify Radical Expressions

Simplify the following radical expression.

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

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

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

Recall that 25 and 4 are perfect squares.

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

From here 12 can be factored further.

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

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Example Question #1 : Simplify Radical Expressions

Simplify the following radical expression.

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

Possible Answers:

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

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

$18\sqrt{19}$ $\displaystyle 18\sqrt{19}$

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

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

Correct answer:

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

Explanation:

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

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

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

Recall that 16 and 4 are perfect squares.

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

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Example Question #1 : Simplify Radical Expressions

Simplify the following radical expression.

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

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

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

Recall that 25 and 4 are perfect squares.

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

From here 12 can be factored further.

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

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Example Question #13 : Algebra 3/4

Simplify the following radical expression.

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

Possible Answers:

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

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

$18\sqrt{19}$ $\displaystyle 18\sqrt{19}$

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

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

Correct answer:

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

Explanation:

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

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

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

Recall that 16 and 4 are perfect squares.

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

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Algebra 3/4 : Simplify Radical Expressions

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

All Algebra 3/4 Resources

Example Questions

Example Question #1 : Simplify Radical Expressions

Example Question #1 : Simplify Radical Expressions

Example Question #1 : Simplify Radical Expressions

Example Question #13 : Algebra 3/4

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