Simplify Radical Expressions

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Algebra › Simplify Radical Expressions

Questions 1 - 4

Simplify the following radical expression.

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

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

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

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

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

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

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.

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

Simplify the following radical expression.

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

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

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

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

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

$18\sqrt{19}$

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.

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

Simplify the following radical expression.

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

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

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

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

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

$18\sqrt{19}$

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.

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

Simplify the following radical expression.

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

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

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

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

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

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

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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