How do you simplify $- 3 \sqrt{18} + 3 \sqrt{8} - \sqrt{24}$ $-3sqrt18+3sqrt8-sqrt24$ ?

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How do you simplify $- 3 \sqrt{18} + 3 \sqrt{8} - \sqrt{24}$ $-3sqrt18+3sqrt8-sqrt24$ ?

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Answer 1 · 2016-08-11T19:27:10

= $\sqrt{2} (- 3 - 2 \sqrt{3})$ $sqrt2(-3-2sqrt3)$

Explanation:

Find each number as the product of its prime factors and see what we are working with. Factors in pairs have a square root.

$- 3 \sqrt{18} + 3 \sqrt{8} - \sqrt{24}$ $-3sqrt18 +3sqrt8-sqrt24$

= $- 3 \sqrt{(3 \times 3) \times 2} + 3 \sqrt{(2 \times 2) \times 2} - \sqrt{(2 \times 2) \times 2 \times 3}$ $-3sqrt((3xx3)xx2) +3sqrt((2xx2)xx2) -sqrt((2xx2)xx2xx3)$

= $- 3 \times 3 \sqrt{2} + 3 \times 2 \sqrt{2} - 2 \sqrt{2} \sqrt{3}$ $-3xx3color(red)(sqrt2)+3xx2color(red)(sqrt2)-2color(red)(sqrt2)sqrt3$

There is a common factor, factorise:

= $\sqrt{2} (- 9 + 6 - 2 \sqrt{3})$ $color(red)(sqrt2)(-9+6-2sqrt3)$

= $\sqrt{2} (- 3 - 2 \sqrt{3})$ $sqrt2(-3-2sqrt3)$

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How do you simplify $- 3 \sqrt{18} + 3 \sqrt{8} - \sqrt{24}$ $-3sqrt18+3sqrt8-sqrt24$ ?

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How do you simplify −3√18+3√8−√24-3sqrt18+3sqrt8-sqrt24?

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How do you simplify $- 3 \sqrt{18} + 3 \sqrt{8} - \sqrt{24}$ $-3sqrt18+3sqrt8-sqrt24$ ?