How do you simplify $3 \sqrt{18} + 3 \sqrt{12} + 2 \sqrt{27}$ $3sqrt18+3sqrt12+2sqrt27$ ?

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Answer 1 · 2016-08-22T01:01:40

$9 \sqrt{2} + 12 \sqrt{3}$ $9sqrt2 +12sqrt3$

Write each number as the product of its prime factors first.
Look for squares of factors.

$3 \sqrt{18} = 3 \times \sqrt{2 \times 3 \times 3} = 3 \times 3 \sqrt{2}$ $3sqrt18 = 3 xxsqrt(2xx3xx3) = 3xx3sqrt2$

$3 \sqrt{12} = 3 \times \sqrt{2 \times 2 \times 3} = 3 \times 2 \sqrt{3}$ $3sqrt12 = 3 xxsqrt(2xx2xx3) = 3xx2sqrt3$

$2 \sqrt{27} = 2 \times \sqrt{3 \times 3 \times 3} = 2 \times 3 \sqrt{3}$ $2sqrt27 = 2xxsqrt(3xx3xx3) = 2xx3sqrt3$

$3 \sqrt{18} + 3 \sqrt{12} + 2 \sqrt{27}$ $3sqrt18 + 3sqrt12 + 2sqrt27$

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

= $9 \sqrt{2} + 12 \sqrt{3}$ $9sqrt2 + color(red)(12sqrt3)$

How do you simplify 3√18+3√12+2√273sqrt18+3sqrt12+2sqrt27?