How do you multiply #(10 +sqrt20) - (4 - sqrt45)#?

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Answer 1 · 2018-05-05T04:14:12

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#color(red)((10 +sqrt20) - (4 - sqrt45)=6+5 sqrt(5)#

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Given the radical expression: #color(blue)((10 +sqrt20) - (4 - sqrt45)#

Remove the brackets:

#rArr 10 +sqrt(20) - 4 + sqrt45)#

Rewrite radicals as:

#rArr 10+sqrt(4*5)-4+sqrt(9.5#

Use the formula: #color(blue)(sqrt(a*b)=sqrt(a)*sqrt(b)#

#rArr 10+sqrt(4)*sqrt(5)-4+sqrt(9)*sqrt(5#

Simplify after combining the like terms:

#rArr 10-4+sqrt(4)*sqrt(5)+sqrt(9)*sqrt(5#

#rArr 6+sqrt(2^2)*sqrt(5)+sqrt(3^2)*sqrt(5#

Use the formula: #color(blue)(sqrt(a^2)=sqrt(a*a)=a#

#rArr 6+2sqrt(5)+3sqrt(5)#

Use the formula: #color(blue)(a sqrt(n)+b sqrt(n)=(a+b)sqrt(n)#

#rArr 6+(2+3) sqrt(5)#

#rArr 6+5 sqrt(5)#

Hence,

#color(blue)((10 +sqrt20) - (4 - sqrt45)=6+5 sqrt(5)#

is the final answer.