Question 858823
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Hi there,

The Problem:
Simplify this expresso:
{{{-sqrt(3)*(sqrt(15)+sqrt(8))}}}

Solution:
Use the distributive property to clear the parentheses.
{{{-sqrt(3)*(sqrt(15)+sqrt(8))=-sqrt(3)*sqrt(15)-sqrt(3)*sqrt(8)}}}

When multiplying radical expressions with the same index (in this case they are all *square* roots), we 
can combine the factors under the same radical sign. For example, {{{sqrt(3)*sqrt(8)=sqrt(24)}}} because 3*8=24.

Simply using the property.
{{{-sqrt(3)*(sqrt(15)+sqrt(8))=-sqrt(45)-sqrt(24)}}}

We can simplify these radical expressions by factoring out any perfect square numbers. For example,
{{{sqrt(45)=sqrt(9*5)=sqrt(9)*sqrt(5)= 3sqrt(5)}}}. (The square root of 9 is 3 because 3*3 = 9.)

Simplify using this property.
{{{-sqrt(3)*(sqrt(15)+sqrt(8))=-3sqrt(5)-sqrt(4*6)=-3sqrt(5)-2sqrt(6)}}}

Hope this helps. Feel free to email me if you have questions about this solution.

Mrs. Figgy
math.in.the.vortex@gmail.com
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