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.

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