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# simplify (3 root 2 + root 5) (3 root 2 - root 5)

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simplify (3 root 2 + root 5) (3 root 2 - root 5)

Guest Aug 8, 2014

#2
+94085
+5

You can do this by a normal expansion if you want but it is a difference of 2 squares and you should commit this to memory.

$$\boxed{(a+b)(a-b)=a^2-b^2}$$

So for your question the simplification will be

$$\\(3 \sqrt2 + \sqrt5) (3 \sqrt2 - \sqrt5)\\\\ =(3 \sqrt2)^2-(\sqrt5)^2\\\\ =3^2 (\sqrt2)^2-(\sqrt5)^2\\\\ =9*2-5\\\\ =18-5\\\\ =13$$

Melody  Aug 9, 2014
#1
+92368
+5

(3√2 +√5) * (3√2 - √5) =

(√18 + √5) * ( √18 - √5) =

18 - 5 =

13

CPhill  Aug 8, 2014
#2
+94085
+5

You can do this by a normal expansion if you want but it is a difference of 2 squares and you should commit this to memory.

$$\boxed{(a+b)(a-b)=a^2-b^2}$$

So for your question the simplification will be

$$\\(3 \sqrt2 + \sqrt5) (3 \sqrt2 - \sqrt5)\\\\ =(3 \sqrt2)^2-(\sqrt5)^2\\\\ =3^2 (\sqrt2)^2-(\sqrt5)^2\\\\ =9*2-5\\\\ =18-5\\\\ =13$$

Melody  Aug 9, 2014
#3
0

Following cphills reply. The reaso  is 3 out sidr the squareroot sign is squared when it is put back in side. This us the opposite when taking the 3 out in surds. Then any two sqyare roots that are the same such as root 2 and root 2 when multiplied become 2. Hope this helps with the post and where the information was provided from. Lastly he has just done this to get whole numbers for the simplest solution. Stu

Guest Aug 10, 2014