How do you simplify sqrt(20d) + 4sqrt(12d) - 3 sqrt(45d)?

2 Answers
EZ as pi
Aug 15, 2017

=8sqrt(3d) -7sqrt(5d)

Explanation:

Write each radicand as the product of its factors and try to find squares wherever possible:

sqrt(20d)+4sqrt(12d) -3sqrt(45d)

=sqrt(4xx5d)+4sqrt(4xx3d) -3sqrt(9xx5d)" "larr find the roots

=2sqrt(5d)+4xx2sqrt(3d) -3xx3sqrt(5d)

=2sqrt(5d)+8sqrt(3d) -9sqrt(5d)" "larr collect like terms

=8sqrt(3d) -7sqrt(5d)

Johnny L.
Aug 15, 2017

After simplifying, you are left with 8sqrt(3d)-7sqrt(5d)

Explanation:

First, let's simplify the numbers under the square root.

sqrt(20)

This can be rewritten as sqrt(4*5)

4 has a square root, so we can pull its square root out of the radical, giving us 2sqrt(5)

Now we do the same thing to sqrt(12) and sqrt(45)

sqrt(12)=sqrt(4*3)=2sqrt(3)

sqrt(45)=sqrt(9*5)=3sqrt(5)

We can't do much with the sqrt(d), so at this point we have:

2sqrt(5d)+4*2sqrt(3d)-3*3sqrt(5d)

After multiplication, we have:

2sqrt(5d)+8sqrt(3d)-9sqrt(5d)

We have two sqrt(5d) terms, so we can combine them, giving us the final answer of:

8sqrt(3d)-7sqrt(5d)

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