How do you simplify 2sqrt54+5sqrt24?

2 Answers
Apr 24, 2018

16sqrt{6}

Explanation:

2sqrt{54} + 5sqrt{24}

54 = 2 times 3^3
24 = 2^3 times 3

2sqrt{2 times 3^3} + 5sqrt{2^3 times 3}

2 sqrt{ 3^2} sqrt{2 times 3}+ 5sqrt{2^2}sqrt{2 times 3}

(2 times 3) sqrt{2 times 3}+ (5 times 2)sqrt{2 times 3}

6sqrt{2 times 3} + 10sqrt{2 times 3}

6sqrt{6} + 10sqrt{6}

(6+10)sqrt{6}

16sqrt{6}

Apr 24, 2018

= 16sqrt6

Explanation:

Write the radicand as a product of its factors, if possible using a square number,

2sqrt54 +5sqrt24

=2sqrt(color(blue)(9)xx6) +5sqrt(color(red)(4)xx6)

=2xxcolor(blue)(3)sqrt6 +5 xx color(red)(2)sqrt6" "larr find the roots

=6sqrt6 +10sqrt6" "larr there are like terms

= 16sqrt6