How do you simplify $30 \sqrt{18} - 15 \sqrt{50}$ $30sqrt18-15sqrt50$ ?

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How do you simplify $30 \sqrt{18} - 15 \sqrt{50}$ $30sqrt18-15sqrt50$ ?

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Answer 1 · 2016-06-01T13:23:57

$= 15 \sqrt{2}$ $= color(Blue)(15 sqrt2$

Explanation:

$30 \sqrt{18} - 15 \sqrt{50}$ $30 color(Blue)(sqrt18) -15 color(blue)(sqrt 50$

We simplify $\sqrt{18}$ $color(blue)(sqrt18$ and $\sqrt{50}$ $color(blue)(sqrt50$ by prime factorisation. (expressing a number as a product of prime factors).

$\sqrt{18} = \sqrt{3 \cdot 3 \cdot 2} = \sqrt{3^{2} \cdot 2} = 3 \sqrt{2}$ $sqrt18 = sqrt ( 3 * 3 * 2 ) = sqrt ( 3^2 * 2) = color(blue)(3 sqrt2$
$\sqrt{50} = \sqrt{2 \cdot 5 \cdot 5} = \sqrt{5^{2} \cdot 2} = 5 \sqrt{2}$ $sqrt50 = sqrt ( 2 * 5 * 5 ) = sqrt ( 5^2 * 2) = color(blue)(5 sqrt2$

The expression now becomes:

$30 \sqrt{18} - 15 \sqrt{50} = 30 \cdot 3 \sqrt{2} - 15 \cdot 5 \sqrt{2}$ $30 color(Blue)(sqrt18) -15 color(blue)(sqrt 50) = 30 * color(blue)(3 sqrt2) -15 * color(blue)(5 sqrt2$

$= 90 \sqrt{2} - 75 \sqrt{2}$ $= 90sqrt2 - 75sqrt2$

Since $\sqrt{2}$ $sqrt2$ is common to both terms we take it out as a common term,

$= \sqrt{2} (90 - 75)$ $= sqrt2 ( 90 - 75)$

$= \sqrt{2} (15)$ $= sqrt2 (15)$

$= 15 \sqrt{2}$ $= color(Blue)(15 sqrt2$

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How do you simplify $30 \sqrt{18} - 15 \sqrt{50}$ $30sqrt18-15sqrt50$ ?

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How do you simplify 30√18−15√5030sqrt18-15sqrt50?

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How do you simplify $30 \sqrt{18} - 15 \sqrt{50}$ $30sqrt18-15sqrt50$ ?